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

 

SVEP for multipliers on a faithful commutative Banach algebra


Authors: Janko Bracic and Martin Jesenko
Journal: Proc. Amer. Math. Soc. 135 (2007), 3181-3185
MSC (2000): Primary 47B40, 47B48
Published electronically: May 10, 2007
MathSciNet review: 2322748
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Abstract: We give some sufficient conditions that each multiplier on a faithful commutative Banach algebra has SVEP. On the other hand, we show that there exist a faithful commutative Banach algebra and a multiplier on it without SVEP. Such examples of multipliers can actually be found within the class of multiplication operators on unital commutative Banach algebras. This answers in negative a question that is stated as Open problem 6.2.1 by Laursen and Neumann, 2000.


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Additional Information

Janko Bracic
Affiliation: University of Ljubljana, IMFM, Jadranska ul. 19, SI-1000 Ljubljana, Slovenia
Email: janko.bracic@fmf.uni-lj.si

Martin Jesenko
Affiliation: University of Ljubljana, FMF, Jadranska ul. 19, SI-1000 Ljubljana, Slovenia
Email: martin.jesenko@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08826-0
PII: S 0002-9939(07)08826-0
Keywords: Faithful commutative Banach algebra, multiplier, SVEP
Received by editor(s): March 24, 2006
Received by editor(s) in revised form: June 13, 2006
Published electronically: May 10, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society