Weyl type theorems for $p$-hyponormal and $M$-hyponormal operators
Tom 163 / 2004
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 $f(T)$.
