# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Weyl type theorems for $p$-hyponormal and $M$-hyponormal operators

### Tom 163 / 2004

Studia Mathematica 163(2004), 177-188 MSC: 47A10, 47A53, 47A55. DOI: 10.4064/sm163-2-5

#### Streszczenie

“Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and “generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If $T$ or $T^*$ is $p$-hyponormal or $M$-hyponormal then for every $f\in H(\sigma (T))$, generalized Weyl's theorem holds for $f(T)$, so Weyl's theorem holds for $f(T)$, where $H(\sigma (T))$ denotes the set of all analytic functions on an open neighborhood of $\sigma (T)$. Moreover, if $T^*$ is $p$-hyponormal or $M$-hyponormal then for every $f\in H(\sigma (T))$, generalized a-Weyl's theorem holds for $f(T)$ and hence a-Weyl's theorem holds for $f(T)$.

#### Autorzy

• Xiaohong CaoCollege of Mathematics and
Information Science
Shaanxi Normal University
Xi'an, 710062, P.R. China
e-mail
• Maozheng GuoLMAM, School of Mathematical Sciences
Peking University
Beijing, 100871, P.R. China
• Bin MengLMAM, School of Mathematical Sciences
Peking University
Beijing, 100871, P.R. China

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