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One-sided invertibility of discrete operators with bounded coefficients
Aequationes Mathematicae ( IF 0.9 ) Pub Date : 2021-01-28 , DOI: 10.1007/s00010-020-00773-8
Luis Eduardo Flores-Zapotitla , Yuri I. Karlovich

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.



中文翻译:

有限系数离散算子的单面可逆性

对于\(p \ in(1,\ infty)\),我们为离散带主导的算子建立了空间\(l ^ p = l ^ p(\ mathbb {Z})\)上的单侧可逆性的几个标准是绝对收敛的序列\(\ sum _ {k \ in \ mathbb {Z}} a_k V ^ k \)或形式为\(A = \ sum _ {k \ in F} a_kV ^ k \),其中F\(\ mathbb {Z} \)\(a_k \ in l ^ \ infty \)的有限子集,等距算子V在函数\(f \ in l ^ p中给出\)\((Vf)(n)= f(n + 1)\)表示所有\(n \ in \ mathbb {Z} \)。我们还获得了空间\(l ^ p \)\(p \ in(1,\ infty)\)上的单侧可逆性的充分条件,用于所谓的E调制和倾斜主导的离散Wiener型算子。

更新日期:2021-01-28
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