B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch; H. Zguitti

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Displaying similar documents to “B-Fredholm and Drazin invertible operators through localized SVEP”

A note on the $a$ -Browder’s and $a$ -Weyl’s theorems

M. Amouch, H. Zguitti (2008)

Mathematica Bohemica

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Let $T$ be a Banach space operator. In this paper we characterize $a$ -Browder’s theorem for $T$ by the localized single valued extension property. Also, we characterize $a$ -Weyl’s theorem under the condition $E^{a} (T) = π^{a} (T),$ where $E^{a} (T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $π^{a} (T)$ is the set of all left poles of $T .$ Some applications are also given.

Extended Weyl type theorems

M. Berkani, H. Zariouh (2009)

Mathematica Bohemica

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An operator $T$ acting on a Banach space $X$ possesses property $(gw)$ if $σ_{a} (T) ∖ σ_{{SBF}_{+}^{-}} (T) = E (T),$ where $σ_{a} (T)$ is the approximate point spectrum of $T$ , $σ_{{SBF}_{+}^{-}} (T)$ 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 $(b)$ and $(gb)$ in connection with Weyl type theorems, which are analogous respectively to Browder’s theorem and generalized Browder’s theorem. Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space...

Spectra originating from semi-B-Fredholm theory and commuting perturbations

Qingping Zeng, Qiaofen Jiang, Huaijie Zhong (2013)

Studia Mathematica

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Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if $σ_{d s c} (T + F) = σ_{d s c} (T)$ for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used...

Restriction of an operator to the range of its powers

M. Berkani (2000)

Studia Mathematica

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Let T be a bounded linear operator acting on a Banach space X. For each integer n, define $T_{n}$ to be the restriction of T to $R (T^{n})$ viewed as a map from $R (T^{n})$ into $R (T^{n})$ . In [1] and [2] we have characterized operators T such that for a given integer n, the operator $T_{n}$ is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where $T_{n}$ belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with...

A note on preservation of spectra for two given operators

Carlos Carpintero, Alexander Gutiérrez, Ennis Rosas, José Sanabria (2020)

Mathematica Bohemica

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We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators...

A characterization of some subsets of S-essential spectra of a multivalued linear operator

Teresa Álvarez, Aymen Ammar, Aref Jeribi (2014)

Colloquium Mathematicae

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We characterize some S-essential spectra of a closed linear relation in terms of certain linear relations of semi-Fredholm type.

Displaying similar documents to “B-Fredholm and Drazin invertible operators through localized SVEP”

A note on the a -Browder’s and a -Weyl’s theorems

Extended Weyl type theorems

Spectra originating from semi-B-Fredholm theory and commuting perturbations

Restriction of an operator to the range of its powers

A note on preservation of spectra for two given operators

A characterization of some subsets of S-essential spectra of a multivalued linear operator

A note on the $a$ -Browder’s and $a$ -Weyl’s theorems