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Closed subalgebras of homogeneous Banach algebras

Published online by Cambridge University Press:  09 April 2009

Ching-Nan Tseng  and
Hawi-Chiuan Wang
Ching-Nan Tseng
Affiliation:
Institute of Mathematics National Tsing Hua UniversityTaiwan, Republic of China.
Hawi-Chiuan Wang
Affiliation:
Institute of Mathematics National Tsing Hua UniversityTaiwan, Republic of China.
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Abstract

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Rudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 366 - 376
Copyright
Copyright © Australian Mathematical Society 1975

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