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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Linear maps determining the norm topology


Author: Krzysztof Jarosz
Journal: Trans. Amer. Math. Soc. 353 (2001), 723-731
MSC (2000): Primary 46B03, 46J10; Secondary 46E15
Published electronically: October 11, 2000
MathSciNet review: 1804514
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Abstract:

Let $A$ be a Banach function algebra on a compact space $X$, and let $a\in A$ be such that for any scalar $\lambda $ the element $a+\lambda e$ is not a divisor of zero. We show that any complete norm topology on $A$ that makes the multiplication by $a$ continuous is automatically equivalent to the original norm topology of $A$. Related results for general Banach spaces are also discussed.


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Additional Information

Krzysztof Jarosz
Affiliation: Department of Mathematics, Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026
Email: kjarosz@siue.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02696-9
PII: S 0002-9947(00)02696-9
Keywords: Automatic continuity, uniqueness of norm
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: May 12, 1999
Published electronically: October 11, 2000
Article copyright: © Copyright 2000 American Mathematical Society