# zbMATH — the first resource for mathematics

Weyl’s theorem holds for algebraically hyponormal operators. (English) Zbl 0953.47018
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 $$\sigma(T)$$.

##### MSC:
 47B20 Subnormal operators, hyponormal operators, etc. 47A10 Spectrum, resolvent 47A53 (Semi-) Fredholm operators; index theories
##### Keywords:
algebraically hyponormal operators; Weyl’s theorem
Full Text: