Commutative Banach algebras with non-unique complete norm topology

Author:

Loy Richard J.

Abstract

It has recently been shown that discontinuous functional calculi exist for certain commutative Banach algebras. Such an algebra thus possesses two distinct calculi so that there exist analytic functions whose action on the algebra is not uniquely determined. In this note a method is given for constructing commutative Banach algebras which admit two inequivalent complete norm topologies and the result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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