Linear maps determining the norm topology
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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.References
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Additional Information
- Krzysztof Jarosz
- Affiliation: Department of Mathematics, Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026
- MR Author ID: 93850
- Email: kjarosz@siue.edu
- Received by editor(s): May 14, 1998
- Received by editor(s) in revised form: May 12, 1999
- Published electronically: October 11, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 723-731
- MSC (2000): Primary 46B03, 46J10; Secondary 46E15
- DOI: https://doi.org/10.1090/S0002-9947-00-02696-9
- MathSciNet review: 1804514