We 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 Mf(σ(S)) ⊂ σ(M) where Mf 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 Zk.
@article{1329,
title = {Spectral results for operators commuting with translations on Banach spaces of sequences on Z and Z+},
journal = {CUBO, A Mathematical Journal},
volume = {14},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/1329}
}
Petkova, Violeta. Spectral results for operators commuting with translations on Banach spaces of sequences on Zᴷ and Z⁺. CUBO, A Mathematical Journal, Tome 14 (2012) . http://gdmltest.u-ga.fr/item/1329/