A note on generalized invertibility and invariants of infinite matrices

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