Weyl's theorem for algebrascally $wF(p, r, q)$ operators with $p, q > 0$ and $q \geq 1$
If $T$ or $T*$ is an algebraically $wF(p, r, q)$ operator with $p, r > 0$ and $q ≥ 1$ acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for $f(T)$, for every $f \in \text{Hol}(\sigma(T))$, where $ \text{Hol}(\sigma(T))$ denotes the set of all...
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| Datum: | 2011 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2787 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | If $T$ or $T*$ is an algebraically $wF(p, r, q)$ operator with $p, r > 0$ and $q ≥ 1$ acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for $f(T)$, for every $f \in \text{Hol}(\sigma(T))$,
where $ \text{Hol}(\sigma(T))$ denotes the set of all analytic functions in an open neighborhood of $\sigma(T)$.
Moreover, if $T^*$ is a $wF(p, r, q)$ operator with $p, r > 0$ and $q ≥ 1$, then the $a$-Weyl theorem holds for $f(T)$. Also, if $T$ or $T^*$ is an algebraically $wF(p, r, q)$ operators with $p, r > 0$ and $q ≥ 1$, then we establish spectral mapping
theorems for the Weyl spectrum and essential approximate point spectrum of T for every $f \in \text{Hol}(\sigma(T))$, respectively. Finally, we examine the stability of the Weyl theorem and $a$-Weyl theorem under commutative perturbation by finite-rank operators. |
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