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Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices
Arabian Journal of Mathematics ( IF 0.9 ) Pub Date : 2018-08-27 , DOI: 10.1007/s40065-018-0220-x
Mohammad Hussein Mohammad Rashid

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 AB, 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:

上三角算子矩阵的广义Weyl定理和性质(gw)

众所周知,如果\(A \ in \ mathscr {L}(\ mathscr {X})\)\(B \ in \ mathscr {L}(\ mathscr {Y})\)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\(M_0 \)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TS,以便\(T \ oplus S \)服从属性(gw)。
更新日期:2018-08-27
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