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A note on strong Ditkin algebras

Published online by Cambridge University Press:  17 April 2009

J.F. Feinstein
J.F. Feinstein
Affiliation:
Department of MathematicsThe University of NottinghamNottingham NG7 2RDEngland, e-mail: jff@maths.nottingham.ac.uk
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Abstract

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In this note we answer a question of W. G. Bade by showing that if a normal, unital Banach function algebra A is strongly regular at one of its characters φ has a bounded approximate identity, then A has bounded relative units at φ. In particular, every strong Ditkin algebra has bounded relative units at all points of its character space. There need not, however, be a global bound available for the relative units.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 25 - 30
Copyright
Copyright © Australian Mathematical Society 1995

References

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