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Translation invariance, compact semigroups and injective coalgebras

Published online by Cambridge University Press:  24 October 2008

Andrew M. Tonge
Andrew M. Tonge
Affiliation:
Université de Paris-Sud, Orsay, France; St John's College, Cambridge
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Extract

The lack of a satisfactory notion of the dual of a compact semigroup S precludes a simple concrete characterization of the closed translation invariant subspaces of C(S). In this article we develop an abstract theory of such spaces (satisfying a weak version of the Banach approximation property) in terms of ‘injective coalgebras’. We characterize their dual spaces as those Banach algebras whose closed unit balls are compact semigroups under the weak star topology. Injective Hopf algebras are shown to be the spaces C(G), G a compact group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 225 - 236
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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