Multipliers on compact groups
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- by Charles F. Dunkl and Donald E. Ramirez PDF
- Proc. Amer. Math. Soc. 28 (1971), 456-460 Request permission
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.References
- Charles F. Dunkl and Donald E. Ramirez, Translation in measure algebras and the correspondence to Fourier transforms vanishing at infinity, Michigan Math. J. 17 (1970), 311–319. MR 283585
- Marc A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Functional Analysis 1 (1967), 443–491. MR 0223496, DOI 10.1016/0022-1236(67)90012-2
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 456-460
- MSC: Primary 46.80; Secondary 42.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276791-1
- MathSciNet review: 0276791