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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-1974-0326453-X

Keywords:
Hilbert space,
operator,
spectrum,
numerical range,
canonical image,
cramped unitary operator,
compact operator

Article copyright:
© Copyright 1974
American Mathematical Society