Journal of Operator Theory
Volume 63, Issue 2, Spring 2010 pp. 283-300.
Multipliers and Toeplitz operators on Banach spaces of sequencesAuthors: Violeta Petkova
Author institution: LABAG, Univ. Bordeaux I, 351, Cours de la Liberation, 33405 Talence, France; Actual address: LMAM, Universite de Metz, Ile du Saulcy, 57045, Metz, France
Summary: In this paper we prove that every multiplier M (every bounded operator commuting with the shift operator S) on a large class of Banach spaces of sequences on \Z is associated to a function essentially bounded by ‖ on \mathrm{spec}(S). This function is holomorphic on \overset{\circ}{\mathrm{spec}}(S) if \overset{\circ}{\mathrm{spec}}(S)\neq \emptyset. Moreover, we give a simple description of \mathrm{spec}(S). We also obtain similar results for Toeplitz operators on a large class of Banach spaces of sequences on~\Z^+.
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