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.