One-sided invertibility of discrete operators with bounded coefficients

Abstract

For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either absolutely convergent series $$\sum _{k\in \mathbb {Z}}a_k V^k$$ or uniform limits of band operators of the form $$A=\sum _{k\in F} a_kV^k$$ , where F is a finite subset of $$\mathbb {Z}$$ , $$a_k\in l^\infty $$ , and the isometric operator V is given on functions $$f\in l^p$$ by $$(Vf)(n) =f(n+1)$$ for all $$n\in \mathbb {Z}$$ . We also obtain sufficient conditions of one-sided invertibility on spaces $$l^p$$ with $$p\in (1,\infty )$$ for the so-called E-modulated and slant-dominated discrete Wiener-type operators.