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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 ${\bigcap }_{C\in ℬ\left(K,H\right)}{\sigma }_{ab}\left({M}_{C}\right)$, ${\bigcap }_{C\in ℬ\left(K,H\right)}{\sigma }_{sb}\left({M}_{C}\right)$ and ${\bigcap }_{C\in ℬ\left(K,H\right)}{\sigma }_{b}\left({M}_{C}\right)$, where ${\sigma }_{ab}\left(·\right)$, ${\sigma }_{sb}\left(·\right)$ and ${\sigma }_{b}\left(·\right)$ are the upper semi-Browder spectrum, the lower semi-Browder spectrum and the Browder spectrum, respectively; here, ${M}_{C}=\left(\begin{array}{cc}A& C\\ 0& B\end{array}\right)$ denotes an upper triangular operator matrix acting on the Hilbert space $H\oplus K$. They also present a revised version of Theorem 8 in [X. Fang, Adv. Math. 186, No. 2, 411–437 (2004; Zbl 1070.47007)].
##### MSC:
 47A10 Spectrum and resolvent of linear operators 47A53 (Semi-)Fredholm operators; index theories