Weyl’s theorem holds for algebraically hyponormal operators

Han, Young Min; Lee, Woo

doi:10.1090/S0002-9939-00-05741-5

Weyl’s theorem holds for algebraically hyponormal operators
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by Young Min Han and Woo Young Lee PDF

Proc. Amer. Math. Soc. 128 (2000), 2291-2296 Request permission

Abstract:

In this note it is shown that if $T$ is an “algebraically hyponormal" operator, i.e., $p(T)$ is hyponormal for some nonconstant complex polynomial $p$, then for every $f\in H(\sigma (T))$, Weyl’s theorem holds for $f(T)$, where $H(\sigma (T))$ denotes the set of analytic functions on an open neighborhood of $\sigma (T)$.

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