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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multipliers on compact groups

Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Proc. Amer. Math. Soc. 28 (1971), 456-460
MSC: Primary 46.80; Secondary 42.00
MathSciNet review: 0276791
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Abstract: Let a compact group $ G$ act continuously both by left and right translation on a Banach space $ V$ of integrable functions on $ G$. Then $ \mathfrak{M}(V)$, the space of bounded linear operators on $ V$ commuting with right translation, contains a homomorphic image of $ {L^1}(G)$, whose closure is exactly the set of operators on which $ G$ acts continuously. Further, this set is exactly the ideal of compact operators in $ \mathfrak{M}(V)$. A restricted version holds for noncompact groups.

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Keywords: Intertwining operators, translation continuous, multiplier algebra, compact operator
Article copyright: © Copyright 1971 American Mathematical Society