Abstract
The following problem was posed by D. A. Herrero in[7]: “Is the multiplicity of the commutant of operators a quasisimilarity invariant?”. Studying this question it is shown that this multiplicity is constant, actually, it is 1, in the quasisimilarity orbits of normal operators, C - contractions, weak contractions and of isometries whose completely non-° unitary parts are of finite multiplicity. Finally, an operator T is constructed, with commutant of infinite multiplicity, so that T is “close” to the quasisimilarity orbit of the unilateral shift of infinite multiplicity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.