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

International audienceWe study the spectrum of multipliers (bounded operators commuting with the shift operator S) on a Banach space E of sequences on Z. Given a multiplier M , we prove that f M (σ(S)) ⊂ σ(M) where f M is the symbol of M. We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on Z +. We generalize the results for multipliers on Banach spaces of sequences on Z k