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.
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The work was partially supported by the SEP-CONACYT Projects A1-S-8793 and A1-S-9201 (México). The first author was also sponsored by the CONACYT Scholarship No. 788493.
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Flores-Zapotitla, L.E., Karlovich, Y.I. One-sided invertibility of discrete operators with bounded coefficients. Aequat. Math. 95, 699–735 (2021). https://doi.org/10.1007/s00010-020-00773-8
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DOI: https://doi.org/10.1007/s00010-020-00773-8
Keywords
- One-sided and two-sided invertibility
- Discrete band-dominated operator
- E-Modulated discrete Wiener-type operator
- Slant-dominated discrete Wiener-type operator
- Lower norm