Weyl's type theorems and perturbations.
Aiena, P., Guillen, J.R., Peña, P. (2008)
Divulgaciones Matemáticas
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Aiena, P., Guillen, J.R., Peña, P. (2008)
Divulgaciones Matemáticas
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H. Zariouh (2013)
Matematički Vesnik
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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...
Aiena, Pietro, Carpintero, Carlos, Rosas, Ennis (2007)
Divulgaciones Matemáticas
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Mohamed Amouch (2006)
Extracta Mathematicae
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Let T be a bounded linear operator acting on a Banach space X such that T or T* has the single-valued extension property (SVEP). We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum σ(T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of σ(T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application...
Christoph Schmoeger (1998)
Extracta Mathematicae
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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.
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 ∈...
M. Berkani, H. Zariouh (2010)
Matematički Vesnik
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Anuradha Gupta, Neeru Kashyap (2010)
Matematički Vesnik
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Yang, Youngoh (1998)
International Journal of Mathematics and Mathematical Sciences
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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...