SVEP for multipliers on a faithful commutative Banach algebra
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- by Janko Bračič and Martin Jesenko PDF
- Proc. Amer. Math. Soc. 135 (2007), 3181-3185 Request permission
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.References
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Additional Information
- Janko Bračič
- 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
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3181-3185
- MSC (2000): Primary 47B40, 47B48
- DOI: https://doi.org/10.1090/S0002-9939-07-08826-0
- MathSciNet review: 2322748