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] |

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)]. |