Transactions of the American Mathematical Society

Author(s): Krzysztof Jarosz
Journal: Trans. Amer. Math. Soc. 353 (2001), 723-731.
MSC (2000): Primary 46B03, 46J10; Secondary 46E15
Posted: October 11, 2000
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Let

be a Banach function algebra on a compact space

, 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

that makes the multiplication by

continuous is automatically equivalent to the original norm topology of

. Related results for general Banach spaces are also discussed.

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