Classes of operators satisfying a-Weyl's theorem

Pietro Aiena

Displaying similar documents to “Classes of operators satisfying a-Weyl's theorem”

On generalized a-Browder's theorem

Pietro Aiena, T. Len Miller (2007)

Studia Mathematica

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We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.

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...

On operators T such that Weyl's theorem holds for f(T).

Christoph Schmoeger (1998)

Extracta Mathematicae

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Weyl numbers versus Z-Weyl numbers

Bernd Carl, Andreas Defant, Doris Planer (2014)

Studia Mathematica

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Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), the s-number sequence of Z-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with Z-Weyl numbers-a problem originally posed by A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue...

Weyl's type theorems and perturbations.

Aiena, P., Guillen, J.R., Peña, P. (2008)

Divulgaciones Matemáticas

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Weyl's and Browder's theorems for operators satisfying the SVEP

Mourad Oudghiri (2004)

Studia Mathematica

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We study Weyl's and Browder's theorem for an operator T on a Banach space such that T or its adjoint has the single-valued extension property. We establish the spectral mapping theorem for the Weyl spectrum, and we show that Browder's theorem holds for f(T) for every f ∈ 𝓗 (σ(T)). Also, we give necessary and sufficient conditions for such T to obey Weyl's theorem. Weyl's theorem in an important class of Banach space operators is also studied.

On the theorem of Meusnier in Weyl spaces

A. Szybiak, Trán dinh Vién (1973)

Annales Polonici Mathematici

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a-Weyl's theorem and perturbations

Mourad Oudghiri (2006)

Studia Mathematica

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We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.

Hereditarily normaloid operators.

Bhagwati Prashad Duggal (2005)

Extracta Mathematicae

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A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T ∈ HN, if every part of T is normaloid; T ∈ HN is totally hereditarily normaloid, T ∈ THN, if every invertible part of T is also normaloid; and T ∈ CHN if either T ∈ THN or T - λI is in HN for every complex number λ. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T ∈ CHN, and prove that the Riesz projection associated with a λ ∈ isoσ(T), T ∈...

Single valued extension property and generalized Weyl’s theorem

M. Berkani, N. Castro, S. V. Djordjević (2006)

Mathematica Bohemica

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Let $T$ be an operator acting on a Banach space $X$ , let $σ (T)$ and $σ_{B W} (T)$ be respectively the spectrum and the B-Weyl spectrum of $T$ . We say that $T$ satisfies the generalized Weyl’s theorem if $σ_{B W} (T) = σ (T) ∖ E (T)$ , where $E (T)$ is the set of all isolated eigenvalues of $T$ . The first goal of this paper is to show that if $T$ is an operator of topological uniform descent and $0$ is an accumulation point of the point spectrum of $T,$ then $T$ does not have the single valued extension property at $0$ , extending an earlier result of J. K. Finch...