Vector valued Beurling algebra analogues of Wiener's Theorem
Authors :- PA Dabhi, KB Solanki
Publication :- arXiv Journal, Cornell University, 2022.
Let 0<p≤1, ω be a weight on Z, and let A be a unital Banach algebra. If f is a continuous function from the unit circle T to A such that ∑n∈Z∥fˆ(n)∥pω(n)p<∞ and f(z) is left invertible for all z∈T, then there is a weight ν on Z and a continuous function g:T→A such that 1≤ν≤ω, ν is constant if and only if ω is constant, g is a left inverse of f and ∑n∈Z∥gˆ(n)∥pν(n)p<∞. We shall obtain a similar result when ω is an almost monotone algebra weight and 1<p<∞. We shall obtain an analogue of this result on the real line. We shall apply these results to obtain p−power weighted analogues of the results of off diagonal decay of infinite matrices of operators. Subjects: Functional Analysis (math.FA) MSC classes: 43A50, 46H35 Cite as: arXiv:2210.04444 [math.FA] (or arXiv:2210.04444v1 [math.FA] for this version) https://doi.org/10.48550/arXiv.2210.04444 Focus to learn more