| Title:
|
Extended Weyl type theorems (English) |
| Author:
|
Berkani, M. |
| Author:
|
Zariouh, H. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
369-378 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An operator $T$ acting on a Banach space $X$ possesses property $({\rm gw})$ if $\sigma _a(T)\setminus \sigma _{{\rm SBF}_+^-}(T)= E(T), $ where $\sigma _a(T)$ is the approximate point spectrum of $T$, $\sigma _{{\rm SBF} _+^-}(T)$ is the essential semi-B-Fredholm spectrum of $T$ and $E(T)$ is the set of all isolated eigenvalues of $T.$ In this paper we introduce and study two new properties $({\rm b})$ and $({\rm gb})$ in connection with Weyl type theorems, which are analogous respectively to Browder's theorem and generalized Browder's theorem. \endgraf Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space $X$, then property $({\rm gw})$ holds for $T$ if and only if property $({\rm gb})$ holds for $T$ and $E(T)=\Pi (T),$ where $\Pi (T)$ is the set of all poles of the resolvent of $T.$ (English) |
| Keyword:
|
B-Fredholm operator |
| Keyword:
|
Browder's theorem |
| Keyword:
|
generalized Browder's theorem |
| Keyword:
|
property $({\rm b})$ |
| Keyword:
|
property $({\rm gb})$ |
| MSC:
|
47A10 |
| MSC:
|
47A11 |
| MSC:
|
47A53 |
| idZBL:
|
Zbl 1211.47011 |
| idMR:
|
MR2597232 |
| DOI:
|
10.21136/MB.2009.140669 |
| . |
| Date available:
|
2010-07-20T18:10:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140669 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
