Displaying similar documents to “Weyl spectra and Weyl's theorem”

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...

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 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.

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 ∈...

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...

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.

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 submersions of Weyl manifolds

Fumio Narita (2007)

Colloquium Mathematicae

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We define Weyl submersions, for which we derive equations analogous to the Gauss and Codazzi equations for an isometric immersion. We obtain a necessary and sufficient condition for the total space of a Weyl submersion to admit an Einstein-Weyl structure. Moreover, we investigate the Einstein-Weyl structure of canonical variations of the total space with Einstein-Weyl structure.

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...