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).

中文翻译：

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上三角算子矩阵的广义Weyl定理和性质（gw）

众所周知，如果\（A \ in \ mathscr {L}（\ mathscr {X}）\）和\（B \ in \ mathscr {L}（\ mathscr {Y}）\）是具有单个的Banach运算符值扩展属性SVEP，则矩阵运算符\（M_ \ mathrm {{C}} = \ begin {pmatrix} A＆{} C \\ 0＆{} B \\ \ end {pmatrix} \）具有SVEP每个运算符\（C \ in \ mathscr {L}（\ mathscr {Y}，\ mathscr {X}）\\）因此服从广义Browder定理。本文考虑了算子A，  B和\（M_0 \）的条件，以确保算子\（M_ \ mathrm {{C}} \）的广义Weyl定理和性质（Bw ）。此外，还对Banach空间算子T和S，以便\（T \ oplus S \）服从属性（gw）。