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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multipliers of weighted spaces and reflexivity property


Author: Xavier Dussau
Journal: Proc. Amer. Math. Soc. 133 (2005), 1379-1386
MSC (2000): Primary 47A15, 43A22; Secondary 46E25, 20C20
Published electronically: October 18, 2004
MathSciNet review: 2111962
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Abstract: We prove for some translation-invariant weighted spaces $E$ the following characterization: $T$ is a multiplier of $E$ if and only if $T$ leaves invariant every translation-invariant subspace of $E$. This result is equivalent with the reflexivity of the multiplier algebra of $E$.


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Additional Information

Xavier Dussau
Affiliation: Laboratoire de Mathématiques Pures, Université Bordeaux I, 351, cours de la libération, 33405 Talence Cedex, France
Email: dussau@math.u-bordeaux.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07640-3
PII: S 0002-9939(04)07640-3
Keywords: Multiplier, translation invariant subspace, reflexivity
Received by editor(s): October 15, 2003
Received by editor(s) in revised form: January 2, 2004
Published electronically: October 18, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.