Abstract
It is known that if \(A\in \mathscr {L}(\mathscr {X})\) and \(B\in \mathscr {L}(\mathscr {Y})\) are Banach operators with the single-valued extension property, SVEP, then the matrix operator \(M_\mathrm{{C}}=\begin{pmatrix} A &{} C \\ 0&{} B \\ \end{pmatrix} \) has SVEP for every operator \(C\in \mathscr {L}(\mathscr {Y},\mathscr {X}),\) and hence obeys generalized Browder’s theorem. This paper considers conditions on operators A, B, and \(M_0\) ensuring generalized Weyl’s theorem and property (Bw) for operators \(M_\mathrm{{C}}\). Moreover, certain conditions are explored on Banach space operators T and S so that \(T\oplus S\) obeys property (gw).
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Rashid, M.H.M. Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices. Arab. J. Math. 9, 167–179 (2020). https://doi.org/10.1007/s40065-018-0220-x
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DOI: https://doi.org/10.1007/s40065-018-0220-x