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Approximate Identities for Ideals of Segal Algebras on A Compact Group

✍ Scribed by Yong Zhang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
106 KB
Volume
191
Category
Article
ISSN
0022-1236

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✦ Synopsis

We show that every closed ideal of a Segal algebra on a compact group admits a central approximate identity which has the property, called condition (U), that the induced multiplication operators converge to the identity operator uniformly on compact sets of the ideal. This result extends a known one due to H. Reiter who has considered the problem under the condition that the Segal algebra is symmetric. We prove further that a closed right ideal of a Segal algebra on a compact group admits a left approximate identity satisfying condition (U) if and only if it is approximately complemented as a subspace of the Segal algebra; if in addition the Segal algebra is symmetric, then a closed left ideal admits a right approximate identity satisfying condition (U) if and only if it is approximately complemented.

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