标题： 关于具有多项式非对角衰减的算子值矩阵的逆闭性 显示英文标题

标题： On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay

摘要： 我们给出一个自包含的证明，证明了一个最近建立的$\mathcal{B}(\mathcal{H})$值版本的 Jaffard 引理。也就是说，我们证明了$\mathcal{B}(\mathcal{H})$值矩阵的 Jaffard 代数，其各自元素的算子范数在对角线外多项式衰减，是一个巴拿赫代数，并且在所有有界线性算子的巴拿赫代数$\mathcal{B}(\ell^2(X;\mathcal{H}))$中是逆闭的，其中$\ell^2(X;\mathcal{H})$是平方可和的$\mathcal{H}$值序列的 Bochner 空间。 显示英文摘要

摘要： We give a self-contained proof of a recently established $\mathcal{B}(\mathcal{H})$-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of $\mathcal{B}(\mathcal{H})$-valued matrices, whose operator norms of their respective entries decay polynomially off the diagonal, is a Banach algebra which is inverse-closed in the Banach algebra $\mathcal{B}(\ell^2(X;\mathcal{H}))$ of all bounded linear operators on $\ell^2(X;\mathcal{H})$, the Bochner-space of square-summable $\mathcal{H}$-valued sequences.