On the theorem of Meusnier in Weyl spaces
A. Szybiak, Trán dinh Vién (1973)
Annales Polonici Mathematici
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A. Szybiak, Trán dinh Vién (1973)
Annales Polonici Mathematici
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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.
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.
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.
Christoph Schmoeger (1998)
Extracta Mathematicae
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B.P. Duggal (2002)
Matematički Vesnik
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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...
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...
António M. Caetano (1991)
Forum mathematicum
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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...
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...
Rigal, Laurent (1996)
Beiträge zur Algebra und Geometrie
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Ю.В. Линник (1943)
Matematiceskij sbornik
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Simpson, Todd (1996)
The Electronic Journal of Combinatorics [electronic only]
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Aiena, P., Guillen, J.R., Peña, P. (2008)
Divulgaciones Matemáticas
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António M. Caetano (1990)
Forum mathematicum
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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.
Aiena, Pietro, Biondi, Maria T., Villafañe, Fernando (2007)
Divulgaciones Matemáticas
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Yang, Youngoh (1998)
International Journal of Mathematics and Mathematical Sciences
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