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Displaying similar documents to “Weyl's type theorems and perturbations.”

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.

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 ∈...

Polaroid type operators under perturbations

Pietro Aiena, Elvis Aponte (2013)

Studia Mathematica

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A bounded operator T defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The "polaroid" condition is related to the conditions of being left polaroid, right polaroid, or a-polaroid. In this paper we explore all these conditions under commuting perturbations K. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for T + K,...

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.

Generalized Weyl's theorem and quasi-affinity

Pietro Aiena, Mohammed Berkani (2010)

Studia Mathematica

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A bounded operator T ∈ L(X) acting on a Banach space X is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. We prove that generalized Weyl's theorem holds for several classes of operators, extending previous results of Istrăţescu and Curto-Han. We also consider the preservation of generalized Weyl's theorem between two operators T ∈ L(X), S ∈ L(Y) intertwined or...

Weyl's theorem, a-Weyl's theorem and single-valued extension property.

Pietro Aiena, Carlos Carpintero (2005)

Extracta Mathematicae

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In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the...

Weyl spectra and Weyl's theorem

Young Min Han, Woo Young Lee (2001)

Studia Mathematica

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"Weyl's theorem" for an operator on a Hilbert space is the statement that the complement in the spectrum of the Weyl spectrum coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl's theorem survives for polynomials of operators and under quasinilpotent or compact perturbations. First, we show that if T is reduced by each of its finite-dimensional eigenspaces then the Weyl spectrum obeys the spectral mapping theorem, and further if T is reduction-isoloid...

Classes of operators satisfying a-Weyl's theorem

Pietro Aiena (2005)

Studia Mathematica

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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...

Weyl type theorems for p-hyponormal and M-hyponormal operators

Xiaohong Cao, Maozheng Guo, Bin Meng (2004)

Studia Mathematica

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"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for...