Spectral results for operators commuting with translations on Banach spaces of sequences on Z^k and Z^+

TL;DR

This paper investigates the spectral properties of operators commuting with shift operators on various Banach spaces of sequences, extending known results to higher dimensions and different sequence spaces.

Contribution

It generalizes spectral results for multipliers on Banach spaces of sequences from Z to Z^k and Z^+, providing a broader understanding of these operators.

Findings

Spectral characterization of multipliers on Banach spaces of sequences on Z.

Extension of spectral results to operators on Z^k and Z^+.

Identification of the spectrum for operators commuting with shift operators.

Abstract

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on Banach spaces of sequences on Z and the spectrum of operators commuting with the shift on Banach spaces of sequences on Z^+.We generalize the results for multipliers on Banach spaces of sequences on Z^k.