Kérchy László honlapja

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Cím:On the multiplicity of the commutant of operators. II.
Szerző:K\'erchy, L\'aszl\'o
Forrás:Gheondea, A. (ed.) et al., Topics in operator theory, operator algebras and applications. 15th international conference on operator theory, Timi\c{s}oara, Romania, June 6-10, 1994. Bucharest: Institute of Mathematics of the Romanian Academy. 169-192 (1995). [ISBN 973-0-00189-8]
Nyelv:English
Absztrakt:Summary: It was asked by D. A. Herrero whether the multiplicity of the commutant of Hilbert space operators is invariant under quasisimilarity. Proceeding investigations started in part I [Oper. Theory, Adv. Appl. 29, 233-243 (1988; Zbl 0654.47005)]; it is shown that weak similarity does preserve commutant multiplicity. Inspired by the characterization of quasisimilarity of quasinormal operators given in [{\it K.-Y. Chen}, {\it D. A. Herrero} and {\it P. Y. Wu}, J. Oper. Theory 27, No. 2, 385-412 (1992; Zbl 0807.47015)], the commutant multiplicity of quasinormal operators and their adjoints is determined. This multiplicity is also discussed in the quasisimilarity orbit of an arbitrary isometry. Finally, Herrero's question is tested by 2-dimensional extensions of normal operators, where the commutant multiplicity can be greater than one by a result of {\it D. R. Larson} and {\it W. R. Wogen} in [Integral Equations Oper. Theory 20, No. 3, 325-334 (1994; Zbl 0816.47005)]. 
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