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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Keywords: Hilbert space, operator, spectrum, numerical range, canonical image, cramped unitary operator, compact operator
Article copyright: © Copyright 1974 American Mathematical Society