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

 

Elements in a commutative Banach algebra determining the norm topology


Author: A. R. Villena
Journal: Proc. Amer. Math. Soc. 129 (2001), 1057-1064
MSC (2000): Primary 43A20, 46E25, 46J10, 46J15
Published electronically: November 8, 2000
MathSciNet review: 1709768
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Abstract:

For an element $a$ of a commutative complex Banach algebra $(A,\Vert\cdot\Vert)$ we investigate the following property: every complete norm $\vert\cdot\vert$ on $A$ making the multiplication by $a$ from $(A,\vert\cdot\vert)$ to itself continuous is equivalent to $\Vert\cdot\Vert$.


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Additional Information

A. R. Villena
Affiliation: Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: avillena@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05659-8
PII: S 0002-9939(00)05659-8
Received by editor(s): May 19, 1999
Received by editor(s) in revised form: June 28, 1999
Published electronically: November 8, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society