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M. Amouch, Departement de Mathematiques, Faculte des Sciences Semlalia, B. P: 2390 Marrakech, Morocco, e-mail: m.amouch@ucam.ac.ma; H. Zguitti, Departement de Mathematiques et Informatique, Faculte Pluridisciplinaire de Nador, B. P: 300 Selouane, 62700 Nador, Morocco, e-mail: zguitti@hotmail.com
Abstract: 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.
Keywords: B-Fredholm operator, Drazin invertible operator, single-valued extension property
Classification (MSC 2000): 47A53, 47A55, 47A10, 47A11
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