On operators T such that Weyl's theorem holds for f(T).
Christoph Schmoeger (1998)
Extracta Mathematicae
Similarity:
Christoph Schmoeger (1998)
Extracta Mathematicae
Similarity:
Bhagwati Prashad Duggal (2005)
Extracta Mathematicae
Similarity:
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 ∈...
Young Min Han, Woo Young Lee (2001)
Studia Mathematica
Similarity:
"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...
Xiaohong Cao, Maozheng Guo, Bin Meng (2004)
Studia Mathematica
Similarity:
"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...
Mourad Oudghiri (2004)
Studia Mathematica
Similarity:
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.
S. Djordjević, B. Duggal (2000)
Studia Mathematica
Similarity:
We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.
Duggal, B.P. (2005)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Aiena, Pietro, Biondi, Maria T., Villafañe, Fernando (2007)
Divulgaciones Matemáticas
Similarity:
Kim, An-Hyun, Kim, In Hyoun (2006)
Journal of Inequalities and Applications [electronic only]
Similarity:
Aiena, P., Guillen, J.R., Peña, P. (2008)
Divulgaciones Matemáticas
Similarity:
Slaviša V. Đorđević (1998)
Matematički Vesnik
Similarity:
Yuan, Jiangtao, Gao, Zongsheng (2007)
Journal of Inequalities and Applications [electronic only]
Similarity:
Pietro Aiena, Mohammed Berkani (2010)
Studia Mathematica
Similarity:
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...
Rigal, Laurent (1996)
Beiträge zur Algebra und Geometrie
Similarity:
Pietro Aiena, T. Len Miller (2007)
Studia Mathematica
Similarity:
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.