The classes of band-dominated operators and the subclass of operators in the Wiener algebra \({\mathcal {W}}\) are known to be inverse closed. This paper studies and extends partially known results of that type for one-sided and generalized invertibility. Furthermore, for the operators in the Wiener algebra \({\mathcal {W}}\) invertibility, the Fredholm property and the Fredholm index are known to be independent of the underlying space \(l^p\), \(1\le p\le \infty \). Here this is completed by the observation that even the kernel and a suitable direct complement of the range as well as generalized inverses of operators in \({\mathcal {W}}\) are invariant w.r.t. p.

已知维纳代数\({\mathcal {W}}\)中的带支配算子类和算子子类是逆闭的。本文研究并扩展了该类型的片面和广义可逆性的部分已知结果。此外，对于维纳代数\({\mathcal {W}}\)可逆性中的算子，已知 Fredholm 性质和 Fredholm 指数与基础空间\(l^p\)、\(1\ le p\le \infty \)。在这里，这是通过观察到即使内核和范围的合适的直接补充以及\({\mathcal {W}}\)中运算符的广义逆是不变的 wrt p 来完成的。