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Hilbert space operators with compatible off-diagonal corners

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1-s2.0-S0022123618301411-main.pdf (452.89 KB)

Date

2018-08-15

Authors

Livshits, Leo
MacDonald, Gordon
Marcoux, Laurent W.
Radjavi, Heydar

Advisor

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

Given a complex, separable Hilbert space H, we characterize those operators for which ‖PT(I−P)‖=‖(I−P)TP‖ for all orthogonal projections P on H. When H is finite-dimensional, we also obtain a complete characterization of those operators for which rank(I−P)TP=rankPT(I−P) for all orthogonal projections P. When H is infinite-dimensional, we show that any operator with the latter property is normal, and its spectrum is contained in either a line or a circle in the complex plane.

Description

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.jfa.2018.04.002 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Corners, Normal operators, Reductive operators, Unitary operators

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Citation

URI

https://dx.doi.org/10.1016/j.jfa.2018.04.002
 http://hdl.handle.net/10012/13469

Collections

Waterloo Research
Applied Mathematics
Pure Mathematics