LIST OF PUBLICATIONS

Lajos Molnár

Book

Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Lecture Notes in  Mathematics, Vol. 1895, Springer, 2007.  (link to Springer)

Papers

If you are interested in any of my papers, please send me an email and I will be happy to send you the pdf file

1. Characterization of Jordan-Segal isomorphisms of quantum observables, in preparation.
2. Characterizations of certain means of positive operators, in preparation.
3. Quantum Rényi relative entropies: their symmetries and their essential difference, in preparation.
4. with L. Szilas, On 2-local *-automorphisms of B(H), in preparation.
5. Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence, Acta Sci. Math. Szeged, to appear.
6. Bures isometries between density spaces of $C^*$-algebras, Linear Algebra Appl. 557 (2018), 22-33.
7. Busch-Gudder metric on the cone of positive semidefinite operators and its isometries,Integr. Equ. Oper. Theory 90 (2018),
8. Petz Dénes (1953-2018) (in Hungarian), Érintõ, March 2018. link
9. Algebraic isomorphisms in the descriptions of generalized isometries on spaces of positive definite matrices, RIMS Kokyuroku,
No. 2035 (2017), 94-108.
10. with H.Y. Chen, Gy.P. Gehér, C. N. Liu, D. Virosztek,N. C. Wong, Maps on positive definite operators preserving the quantum $\chi_\alpha^2$-divergence, Lett. Math. Phys. 107 (2017), 2267-2290.
11. On the surjectivity of generalized isometries on the positive definite cone of matrices, Mediterr. J. Math. 14:161 (2017).
12. The arithmetic, geometric and harmonic means in operator algebras and transformations among them, Recent Methods and Research Advances in Operator Theory, Ed. F. Botelho, R. King, and T.S.S.R.K. Rao, 182-193, Contemp. Math., 687, Amer. Math. Soc., Providence, RI, 2017.
13. with M. Gaál,Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence, Period. Math. Hung. 74 (2017), 88-107.
14. A characterization of central elements in $C^*$-algebras, Bull. Austral. Math. Soc. 95 (2017), 138-143.
15. with O. Hatori, Spectral conditions for Jordan *-isomorphisms on operator algebras, Studia Math. 236 (2017), 101-126.
16. Maps on the positive definite cone of a $C^*$-algebra preserving certain quasi-entropies, J. Math. Anal. Appl. 447 (2017), 206-221.
17. The logarithmic function and trace zero elements in finite von Neumann factors, Bull. Austral. Math. Soc. 94 (2016), 290-295.
18. with D. Virosztek,Continuous Jordan triple endomorphisms of $\mathbb P_2$, J. Math. Anal. Appl. 438 (2016), 828–839.
19. with G. Nagy, Spectral order automorphisms on Hilbert space effects and observables: the 2-dimensional case,Lett. Math. Phys. 106 (2016), 535-544.
20. with J. Pitrik and D. Virosztek, Maps on positive definite matrices preserving Bregman and Jensen divergences, Linear Algebra Appl. 495 (2016), 174-189.
21. with O. Hatori, Generalized isometries of the special unitary group, Arch. Math.106 (2016), 155-163.
22. with F. Botelho and G. Nagy, Linear bijections on von Neumann factors commuting with $\lambda$-Aluthge transform, Bull. London Math. Soc. 48 (2016), 74-84.
23. Two characterizations of unitary-antiunitary similarity transformations of positive definite operators on a finite dimensional Hilbert space, Annales Univ. Sci. Budapest., Sect. Comp. (special issue dedicated to Prof. Zoltán Sebestyén on the occasion of his 70th birthday) 58 (2015), 83-93.
24. General Mazur-Ulam type theorems and some applications, in "Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics", W. Arendt, R. Chill, Y. Tomilov (Eds.), Operator Theory: Advances and Applications, Vol. 250, pp. 311-342, Birkhäuser, 2015.
25. with P. Szokol,Transformations preserving norms of means of positive operators and nonnegative functions, Integral Equations Operator Theory 83 (2015), 271-290.
26. with D. Virosztek, On algebraic endomorphisms of the Einstein gyrogroup, J. Math. Phys. 56 (2015), 082302.
27. On the nonexistence of order isomorphisms between the sets of all self-adjoint and all positive definite operators, Abstr. Appl. Anal. Volume 2015 (2015), Article ID 434020, 6 pages.
28. with P. Semrl and A.R. Sourour, Bilocal automorphisms, Oper. Matrices 9 (2015), 113-120.
29. with P. Szokol,Transformations on positive definite matrices preserving generalized distance measures, Linear Algebra Appl. 466 (2015), 141-159.
30. Jordan triple endomorphisms and isometries of spaces of positive definite matrices, Linear Multilinear Algebra 63 (2015), 12-33.
31. with G. Nagy, Transformations on density operators that leave the Holevo bound invariant, Int. J. Theor. Phys. 53 (2014), 3273-3278.
32. with R. Beneduci, On the standard K-loop structure of positive invertible elements in a C*-algebra, J. Math. Anal. Appl. 420 (2014), 551-562.
33. A few conditions for a C*-algebra to be commutative, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 705836, 4 pages.
34. with P. Szokol, Kolmogorov-Smirnov isometries of the space of generalized distribution functions, Math. Slovaca 64 (2014), 433-444.
35. Bilocal *-automorphisms of B(H), Arch. Math.102 (2014), 83-89.
36. with O. Hatori,  Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras,  J. Math. Anal. Appl. 409 (2014), 158-167.
37. Jordan triple endomorphisms and isometries of unitary groups, Linear Algebra Appl. 439 (2013), 3518-3531.
38. with F. Botelho and J. Jamison, Surjective isometries on Grassmann spaces, J. Funct. Anal. 265 (2013), 2226-2238.
39. with F. Botelho and J. Jamison, Algebraic reflexivity of isometry groups and automorphism groups of some operator structures, J. Math. Anal. Appl. 408 (2013), 177-195.
40. with G. Nagy and P. Szokol, Maps on density operators preserving quantum f-divergences, Quantum Inf. Process. 12 (2013), 2309-2323.
41. with G. Dolinar, Automorphisms for the logarithmic product of positive semidefinite operators, Linear Multilinear Algebra 61 (2013), 161-169.
42. with O. Hatori, G. Hirasawa,  and T. Miura, Isometries and maps compatible with inverted Jordan triple products on groups, Tokyo J. Math. 35 (2012), 385-410.
43. with O. Hatori, Isometries of the unitary group, Proc. Amer. Math. Soc. 140 (2012), 2141-2154.
44. with G. Dolinar, Sequential endomorphisms of finite dimensional Hilbert space effect algebras,  J. Phys. A: Math. Theor. 45 (2012) 065207.
45. with P. Semrl, Transformations of the unitary group on a Hilbert space, J. Math. Anal. Appl. 388 (2012), 1205-1217.
46. with G. Nagy, Isometries and relative entropy preserving maps on density operators, Linear Multilinear Algebra 60 (2012), 93-108.
47. Maps preserving general means of positive operators, Electron. J. Linear Algebra 22 (2011), 864-874.
48. Continuous maps on matrices transforming geometric mean to arithmetic mean, Annales Univ. Sci. Budapest., Sect. Comp. 35 (2011) , 217-222. (special issue dedicated to Prof. Antal Járai on the occasion of his 60th birthday)
49. with W. Timmermann, Transformations on bounded observables preserving measure of compatibility, Int. J. Theor. Phys. 50 (2011), 3857-3863.
50. Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions, Cent. Eur. J. Math. 9 (2011), 789-796.
51. Lévy isometries of the space of probability distribution functions, J. Math. Anal. Appl. 380 (2011), 847-852.
52. Order automorphisms on positive definite operators and a few applications, Linear Algebra Appl. 434 (2011), 2158-2169.
53. with P. Szokol, Maps on states preserving the relative entropy II, Linear Algebra Appl. 432 (2010), 3343-3350.
54. with G. Nagy, Thompson isometries on positive operators: The 2-dimensional case, Electron. J. Linear Algebra 20 (2010), 79-89.
55. Linear maps on observables in von Neumann algebras preserving the maximal deviation, J. London Math. Soc. 81 (2010), 161-174.
56. Thompson isometries of the space of invertible positive operators, Proc. Amer. Math. Soc. 137 (2009), 3849-3859.
57. Maps preserving the harmonic mean or the parallel sum of positive operators, Linear Algebra Appl. 430 (2009), 3058-3065.
58. Maps on positive operators preserving Lebesgue decompositions, Electron. J. Linear Algebra 18 (2009), 222-232.
59. with W. Timmermann, A metric on the space of projections admitting nice isometries, Studia Math. 191 (2009), 271-281.
60. Maps preserving the geometric mean of positive operators, Proc. Amer. Math. Soc. 137 (2009), 1763-1770.
61. with W. Timmermann, Maps on quantum states preserving the Jensen-Shannon divergence, J. Phys. A: Math. Theor.  42 (2009), 015301.
62. Linear maps on matrices preserving commutativity up to a factor, Linear Multilinear Algebra 57 (2009), 13-18.
63. with G. Dolinar, Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnov metric,  J. Math. Anal. Appl. 348 (2008), 494-498.
64. Maps on the n-dimensional subspaces of a Hilbert space preserving principal angles, Proc. Amer. Math. Soc. 136 (2008), 3205-3209.
65. Maps on states preserving the relative entropy, J. Math. Phys. 49 (2008), 032114.
66. Isometries of the spaces of bounded frame functions, J. Math. Anal. Appl., 338 (2008), 705-710.
67. with G. Dolinar, Maps on quantum observables preserving the Gudder order, Rep. Math. Phys. 60 (2007), 159-166.
68. with P. Semrl, Spectral order automorphisms of the spaces of Hilbert space effects and observables, Lett. Math. Phys., 80 (2007), 239-255.
69. with W. Timmermann, Mixture preserving maps on von Neumann algebra effects, Lett. Math. Phys., 79 (2007), 295-302.
70. with P. Semrl, Elementary operators on self-adjoint operators, J. Math. Anal. Appl., 327 (2007), 302-309.
71. Multiplicative Jordan triple isomorphisms on the self-adjoint elements of von Neumann algebras, Linear Algebra Appl. 419 (2006), 586-600.
72. with W. Timmermann, Transformations on the sets of states and density operators, Linear Algebra Appl. 418 (2006), 75-84.
73. Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators, Studia Math. 173 (2006), 39-48.
74. A remark to the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices, Proc. Amer. Math. Soc. 134 (2006), 2839-2848.
75. with P. Semrl, Non-linear commutativity preserving maps on self-adjoint operators, Quart. J. Math. 56 (2005), 589-595.
76. with E. Kovács, Preserving some numerical correspondences between Hilbert space effects, Rep. Math. Phys. 54 (2004), 201-209.
77. On transformations of the set of quantum states, in Hungarian, Assembly Lectures, Hungarian Academy of Sciences, Budapest, to appear.
78. Sequential isomorphisms between the sets of von Neumann algebra effects, Acta Sci. Math. (Szeged) 69 (2003), 755-772.
79. with P. Semrl, Conditional affine and conditional sequential automorphisms of the set of Hilbert space effects, unpublished.
80. with E. Kovács, An extension of a characterization of the automorphisms of Hilbert space effect algebras, Rep. Math. Phys. 52 (2003), 141-149.
81. with M. Barczy, Linear maps on the space of all bounded observables preserving maximal deviation, J. Funct. Anal. 205 (2003), 380-400.
82. Preservers on Hilbert space effects, Linear Algebra Appl. 370 (2003), 287-300.
83. with W. Timmermann, Preserving the measure of compatibility between quantum states, J. Math. Phys. 44 (2003), 969-973.
84. with W. Timmermann, Isometries of quantum states, J. Phys. A: Math. Gen. 36 (2003), 267-273.
85. Local automorphisms of operator algebras on Banach spaces, Proc. Amer. Math. Soc. 131 (2003), 1867-1874.
86. with P. Semrl, Elementary operators on standard operator algebras, Linear and Multilinear Algebra 50 (2002), 315-319.
87. Orthogonality preserving transformations on indefinite inner product spaces: generalization of Uhlhorn's version of Wigner's theorem, J. Funct. Anal. 194 (2002), 248-262.
88. with F. Cabello Sánchez, Reflexivity of the isometry group of some classical spaces, Rev. Mat. Iberoam. 18 (2002), 409-430.
89. 2-local isometries of some operator algebras, Proc. Edinb. Math. Soc. 45 (2002), 349-352.
90. Conditionally multiplicative maps on the set of all bounded observables preserving compatibility, Linear Algebra Appl. 349 (2002), 197-201.
91. On certain automorphisms of sets of partial isometries, Arch. Math. 78 (2002), 43-50.
92. Some characterizations of the automorphisms of B(H) and C(X), Proc. Amer. Math. Soc. 130 (2002), 111-120.
93. Jordan maps on standard operator algebras, in Z. Daróczy and Zs. Páles (Edt.), Functional Equations -- Results and Advances, pp. 305-320, Kluwer Academic Publishers, 2001.
94. Local automorphisms of some quantum mechanical structures, Lett. Math. Phys. 58 (2001), 91-100.
95. Fidelity preserving maps on density operators, Rep. Math. Phys. 48 (2001), 299-303.
96. Order-automorphisms of the set of bounded observables, J. Math. Phys. 42 (2001), 5904-5909.
97. *-semigroup endomorphisms of B(H), in I. Gohberg et al. (Edt.), Operator Theory: Advances and Applications, Vol. 127, pp. 465-472, Birkhauser, 2001.
98. Characterizations of the automorphisms of Hilbert space effect algebras, Commun. Math. Phys. 223 (2001), 437-450.
99. with Zs. Páles, ${}^\perp$-order automorphisms of Hilbert space effect algebras: The two-dimensional case, J. Math. Phys. 42 (2001), 1907-1912.
100. Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles, Commun. Math. Phys. 217 (2001), 409-421.
101. A reflexivity problem concerning the C*-algebra C(X) x B(H), Proc. Amer. Math. Soc. 129 (2001), 531-537.
102. A Wigner-type theorem on symmetry transformations in Banach spaces, Publ. Math. (Debrecen) 58 (2000), 231-239.
103. with M. Bresar and P. Semrl, Elementary operators II., Acta Sci. Math. (Szeged) 66 (2000), 769-791.
104. On isomorphisms of standard operator algebras, Studia Math. 142 (2000), 295-302.
105. A Wigner-type theorem on symmetry transformations in type II factor, Int. J. Theor. Phys. 39 (2000), 1463-1466.
106. On some automorphisms of the set of effects on Hilbert space, Lett. Math. Phys. 51 (2000), 37-45.
107. with P. Semrl, Local automorphisms of the unitary group and the general linear group on a Hilbert space, Expo. Math. 18 (2000), 231-238.
108. Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces, Commun. Math. Phys. 210(2000), 785-791.
109. Reflexivity of the automorphism and isometry groups of C*-algebras in BDF theory, Arch. Math. 74 (2000), 120-128.
110. Automatic surjectivity of ring homomorphisms on H*-algebras and algebraic differences among some group algebras of compact groups, Proc. Amer. Math. Soc. 12 (2000), 125-134.
111. with B. Zalar, On local automorphism of group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000) 93-99.
112. Multiplicative maps on ideals of operators which are local automorphisms, Acta Sci. Math. (Szeged) 65(1999), 727-736.
113. Some multiplicative preservers on B(H), Linear Algebra Appl. 301 (1999), 1-13.
114. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules, J. Math. Phys. 40 (1999), 5544-5554.
115. with B. Zalar, Reflexivity of the group of surjective isometries on some Banach spaces, Proc. Edinb. Math. Soc. 42 (1999), 17-36.
116. Some linear preserver problems on B(H) concerning rank and corank, Linear Algebra Appl. 286 (1999), 311-321.
117. An algebraic approach to Wigner's unitary-antiunitary theorem, J. Austral. Math. Soc. 65 (1998), 354-369.
118. with P. Semrl, Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra 45 (1998), 189-206.
119. with V. Mascioni, Linear maps on factors which preserve the extreme points of the unit ball, Canad. Math. Bull. 41(1998), 434-441.
120. The automorphism and isometry groups of l_infinity (N,B(H)) are topologically reflexive, Acta Sci. Math. (Szeged) 64 (1998), 671-680.
121. with M. Gyõry, Reflexivity of the automorphism and isometry groups of the suspension of B(H), J. Funct. Anal. 159 (1998), 568-586.
122. with M. Gyõry, Diameter preserving linear bijections of C(X), Arch. Math. 71 (1998), 301-310.
123. with M. Gyõry and P. Semrl, Linear rank and corank preserving maps on B(H) and an application to *-semigroup isomorphisms of operator ideals, Linear Algebra Appl. 280 (1998), 253-266.
124. Stability of the surjectivity of Jordan *-homomorphisms of B(H), J. Nat. Geom. 14 (1998), 149-154.
125. Characterization of additive *-homomorphisms and Jordan *-homomorphisms on operator ideals, Aequationes Math. 55 (1998), 259-272.
126. A proper standard C*-algebra whose automorphisms and isometry groups are topologically reflexive, Publ. Math. (Debrecen) 52 (1998), 563-574.
127. Stability of the surjectivity of endomorphisms and isometries of B(H), Proc. Amer. Math. Soc. 126 (1998), 853-861.
128. with P. Semrl, Order isomorphisms and triple isomorphisms of operator ideals and their reflexivity, Arch. Math. 69 (1997), 497-506.
129. Jordan *-derivation pairs on a complex *-algebra, Aequationes Math. 54 (1997), 44-55.
130. with B. Zalar, Three-variable *-identities and homomorphisms of Schatten classes, Publ. Math. (Debrecen) 50 (1997), 121-133.
131. The set of automorphisms of B(H) is topologically reflexive in B(B(H)), Studia Math. 122 (1997), 183-193.
132. with P. Semrl, Local Jordan *-derivations of standard operator algebras, Proc. Amer. Math. Soc. 125 (1997), 447-454.
133. On rings of differentiable functions, Grazer Math. Ber. 327 (1996), 13-16.
134. Bijectivity of *-endomorphisms of B(H) and the unilaterial shift, Monatsh. Math. 122 (1996), 377-387.
135. with C.J.K. Batty, On topological reflexivity of the groups of *-automorphisms and surjective isometries of B(H), Arch. Math. 67 (1996), 415-421.
136. The range of a Jordan *-derivation, Math. Japon. 44 (1996), 353-356.
137. The range of a Jordan *-derivation on an H*-algebra, Acta Math. Hung. 72 (1996), 261-267.
138. Wigner's unitary-antiunitary theorem via Herstein's theorem on Jordan homomorphisms, J. Nat. Geom. 10 (1996), 137-148.
139. Two characterizations of additive *-automorphisms of B(H), Bull. Austral. Math. Soc. 53 (1996), 391-400.
140. The range of a ring homomorphism from a commutative C*-algebra, Proc. Amer. Math. Soc. 124 (1996), 1789-1794.
141. Locally inner derivations of standard operator algebras, Math. Bohem. 121 (1996), 1-7.
142. Algebraic difference between p-classes of an H*-algebra, Proc. Amer. Math. Soc. 124 (1996), 169-175.
143. A condition for a subspace of B(H) to be an ideal, Linear Algebra Appl. 235 (1996), 229-234.
144. with B. Zalar, On automatic surjectivity of Jordan homomorphisms, Acta Sci. Math. (Szeged) 61 (1995), 413-424.
145. On centralizers of an H*-algebra, Publ. Math. (Debrecen) 46 (1995), 89-95.
146. Conditions for a function to be a centralizer on an H*-algebra, Acta Math. Hung. 67 (1995), 171-174.
147. On the range of a normal Jordan *-derivation, Comment. Math. Univ. Carolinae 35 (1994), 691-695.
148. A condition for a function to be a bounded linear operator, Indian J. Math. 35 (1993), 1-4.
149. p-classes of an H*-algebra and their representations, Acta Sci. Math. (Szeged) 58 (1993), 411-423.
150. On A-linear operators on a Hilbert A-module, Period Math. Hung. 26 (1993), 219-222.
151. On Saworotnow's Hilbert A-modules, Glasnik Mat. 28 (1993), 259-267.
152. Modular bases in a Hilbert A-module, Czech. Math. J. 42 (1992), 649-656.
153. *-representations of the trace-class of an H*-algebra, Proc. Amer. Math. Soc. 115 (1992), 167-170.
154. A note on the strong Schwarz inequality in Hilbert A-modules, Publ. Math. (Debrecen) 40 (1992), 323-325.
155. A note on Saworotnow's representation theorem on positive definite functions, Houston J. Math. 17 (1991), 89-99.
156. Reproducing kernel Hilbert A-modules, Glasnik Mat. 25 (1990), 335-345.
157. with Y. Kakihara, A remark on HS operator valued c.a.g.o.s. measures, Res. Act. Fac. Sci. Engrg. Tokyo Denki Univ. 12 (1990), 13-19.
158. Two applications of the theory of weakly stationary stochastic processes to harmonic analysis, Glasnik Mat. 25 (1990), 209-219.