Samuel multiplicities and Browder spectrum of operator matrices (Q2885143)

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, \(M_C=\left(\begin{smallmatrix} A & C \\ 0 & B \end{smallmatrix}\right)\) denotes an upper triangular operator matrix acting on the Hilbert space \(H\oplus K\). They also present a revised version of Theorem 8 in [\textit{X. Fang}, Adv. Math. 186, No. 2, 411--437 (2004; Zbl 1070.47007)].