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Commutative Banach algebras with non-unique complete norm topology

Published online by Cambridge University Press:  17 April 2009

Richard J. Loy
Richard J. Loy
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT.
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 3 , June 1974 , pp. 409 - 420
Copyright
Copyright © Australian Mathematical Society 1974

References

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