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Samuel multiplicities and Browder spectrum of operator matrices. (English) Zbl 1264.47011
In this paper, the authors use Samuel multiplicities to characterize the sets $\bigcap_{C\in{\mathcal B}(K,H)}\sigma_{ab}(M_C)$, $\bigcap_{C\in{\mathcal B}(K,H)}\sigma_{sb}(M_C)$ and $\bigcap_{C\in{\mathcal B}(K,H)}\sigma_{b}(M_C)$, where $\sigma_{ab}(.)$, $\sigma_{sb}(.)$ and $\sigma_{b}(.)$ are the upper semi-Browder spectrum, the lower semi-Browder spectrum and the Browder spectrum, respectively; here, $M_C=\left(\smallmatrix A & C \\ 0 & B \endsmallmatrix\right)$ denotes an upper triangular operator matrix acting on the Hilbert space $H\oplus K$. They also present a revised version of Theorem 8 in [{\it X. Fang}, Adv. Math. 186, No. 2, 411--437 (2004; Zbl 1070.47007)].

47A10Spectrum and resolvent of linear operators
47A53(Semi-) Fredholm operators; index theories
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