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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Operators with left inverses similar to their adjoints


Author: S. M. Patel
Journal: Proc. Amer. Math. Soc. 41 (1973), 127-131
MSC: Primary 47A65
MathSciNet review: 0322558
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Abstract: The primary object of this paper is to show that if $ T$ is a left invertible operator with a left inverse $ {T_1}$ and if there exists an operator $ S$ such that $ {T^ \ast } = {S^{ - 1}}{T_1}S$ and $ 0 \notin {\text{cl}}(W(S))$, then $ T$ is similar to an isometry.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0322558-7
PII: S 0002-9939(1973)0322558-7
Keywords: Left inverse, cramped operator, normaloid, polar decomposition, numerical range, left essential spectrum
Article copyright: © Copyright 1973 American Mathematical Society