Geodesic
B-Fredholm and Drazin invertible operators through localized SVEP
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 39-49
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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 $\lambda \in \mathbb C$ such that $T$ does not have the single-valued extension property at $\lambda $. 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.
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 $\lambda \in \mathbb C$ such that $T$ does not have the single-valued extension property at $\lambda $. 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.
DOI : 10.21136/MB.2011.141448
Classification : 47A10, 47A11, 47A53, 47A55
Keywords: B-Fredholm operator; Drazin invertible operator; single-valued extension property 
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Amouch, M.; Zguitti, H. B-Fredholm and Drazin invertible operators through localized SVEP. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 39-49. doi: 10.21136/MB.2011.141448

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