Operators with powers essentially similar to those of their adjoints
Author:
S. M. Patel
Journal:
Proc. Amer. Math. Soc. 42 (1974), 243247
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 , where 0 is not in the essential numerical range of S, and K is compact, then for any complex number in the essential spectrum of T, .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919740326453X
PII:
S 00029939(1974)0326453X
Keywords:
Hilbert space,
operator,
spectrum,
numerical range,
canonical image,
cramped unitary operator,
compact operator
Article copyright:
© Copyright 1974
American Mathematical Society
