Single valued extension property and generalized Weyl’s theorem

M. Berkani; N. Castro; S. V. Djordjević

Displaying similar documents to “Single valued extension property and generalized Weyl’s theorem”

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

M. Amouch, H. Zguitti (2008)

Mathematica Bohemica

Similarity:

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

Similarity:

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

Similarity:

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...

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch, H. Zguitti (2011)

Mathematica Bohemica

Similarity:

Let $X$ be a Banach space and $T$ be a bounded linear operator on $X$ . We denote by $S (T)$ the set of all complex $λ \in ℂ$ such that $T$ does not have the single-valued extension property at $λ$ . In this note we prove equality up to $S (T)$ between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.

Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri (2008)

Studia Mathematica

Similarity:

We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{a s c}^{e} (T + F) = σ_{a s c}^{e} (T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...

Classes of operators satisfying a-Weyl's theorem

Pietro Aiena (2005)

Studia Mathematica

Similarity:

In this article Weyl’s theorem and a-Weyl’s theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl’s theorem and a-Weyl’s theorem for T* are equivalent, and analogously, if T* has SVEP then Weyl’s theorem and a-Weyl’s theorem for T are equivalent. From this result we deduce that a-Weyl’s theorem holds for classes of operators for which the quasi-nilpotent...

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

Similarity:

Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f (σ_{W} (T)) \cup z \in ℂ : | z | = 1$ is connected, where $σ_{W} (T)$ denotes the Weyl spectrum of T.

Spectrum of L

W. Marek, K. Rasmussen

Similarity:

CONTENTS0. Motivation, results to be used in the sequel ................51. Slicing $L_{α}$ ’s ..........................................................102. Hereditarily countable, definable elements ................133. Spectrum of L.............................................................154. The width of elements of spectrum ............................195. Non-uniform strong definability ..................................266. Solution to a problem of Wilmers................................327....