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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 powers essentially similar to those of their adjoints


Author: S. M. Patel
Journal: Proc. Amer. Math. Soc. 42 (1974), 243-247
MSC: Primary 47A65
MathSciNet review: 0326453
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Abstract: Let T be an operator on a Hilbert space H. In the present note the following result is obtained:

If T is an operator such that for some integers $ p,q,S{T^{ \ast p}} = {T^q}S + K$, where 0 is not in the essential numerical range of S, and K is compact, then for any complex number $ \lambda $ in the essential spectrum of T, $ {\lambda ^{ \ast p}} = {\lambda ^q}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0326453-X
PII: S 0002-9939(1974)0326453-X
Keywords: Hilbert space, operator, spectrum, numerical range, canonical image, cramped unitary operator, compact operator
Article copyright: © Copyright 1974 American Mathematical Society