Restriction of an operator to the range of its powers

M. Berkani

Displaying similar documents to “Restriction of an operator to the range of its powers”

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch, H. Zguitti (2011)

Mathematica Bohemica

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Let $X$ be a Banach space and $T$ be a bounded linear operator on $X$ . We denote by $S (T)$ the set of all complex $λ \in ℂ$ such that $T$ does not have the single-valued extension property at $λ$ . In this note we prove equality up to $S (T)$ between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.

Operational quantities characterizing semi-Fredholm operators.

Manuel González, Antonio Martinón (1993)

Extracta Mathematicae

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Geometric characteristic of semi-Fredholm operators and their asymptotic behaviour

Jaroslav Zemánek (1984)

Studia Mathematica

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Semi-Fredholm operators and perturbations.

Živković, Snežana (1997)

Publications de l'Institut Mathématique. Nouvelle Série

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Spectra originating from semi-B-Fredholm theory and commuting perturbations

Qingping Zeng, Qiaofen Jiang, Huaijie Zhong (2013)

Studia Mathematica

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Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if $σ_{d s c} (T + F) = σ_{d s c} (T)$ for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used...

A note on the index of $B$ -Fredholm operators

M. Berkani, Dagmar Medková (2004)

Mathematica Bohemica

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From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251–257] we know that if $S$ , $T$ are commuting $B$ -Fredholm operators acting on a Banach space $X$ , then $S T$ is a $B$ -Fredholm operator. In this note we show that in general we do not have $error (S T) = error (S) + error (T)$ , contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist $U, V \in L (X)$ such that $S$ , $T$ , $U$ , $V$ are commuting and $U S + V T = I$ , then $error (S T) = error (S) + error (T)$ , where $error$ stands for the index of a $B$ -Fredholm...

Approximation by Fredholm operators in the metric space of closed operators

L. A. Coburn, A. Lebow (1966)

Rendiconti del Seminario Matematico della Università di Padova

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An Atkinson-type theorem for B-Fredholm operators

M. Berkani, M. Sarih (2001)

Studia Mathematica

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Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only...