Abstract
We show that, given a closed subset E of the unit circle of Lebesgue measure zero, there exists a positive sequence un→∞ with the following property: if T is a Hilbert-space contraction such that σ(T)⊂E and ‖T−n‖=O(un) and rank(I−T⁎T)<∞, then T is a unitary operator. We further show that the condition of measure zero is sharp.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
