Journal of Operator Theory

Volume 63, Issue 2, Spring 2010 pp. 283-300.

Multipliers and Toeplitz operators on Banach spaces of sequences

Authors: 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

$\|M\|$ 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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