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

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DOI:

https://doi.org/10.4067/S0719-06462012000300002

Abstract

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.

Keywords

Multiplier , Toeplitz operator , shift operator , space of sequences , spectrum of multiplier , joint spectrum of translations
  • Violeta Petkova Universit´e Metz UFR MIM, Laboratoire de Mathmatiques et Applications de Metz, UMR 7122, Ile du Saulcy 57045 Metz Cedex 1, France.
  • Pages: 41–57
  • Date Published: 2012-10-01
  • Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal

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Published

2012-10-01

How to Cite

[1]
V. Petkova, “Spectral results for operators commuting with translations on Banach spaces of sequences on Zá´· and Z⁺”, CUBO, vol. 14, no. 3, pp. 41–57, Oct. 2012.

Issue

Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal

Section

Articles