A note on separating families of representations

Barnes, Bruce A.

doi:10.1090/S0002-9939-1983-0677240-X

A note on separating families of representations
HTML articles powered by AMS MathViewer

by Bruce A. Barnes PDF

Proc. Amer. Math. Soc. 87 (1983), 95-98 Request permission

Abstract:

Conditions are given that imply that a separating family of unitary representations of a locally compact group $G$ lifts to a separating family of $^ *$-representations of ${L^1}(G)$.

References

Siegfried Grosser and Martin Moskowitz, Harmonic analysis on central topological groups, Trans. Amer. Math. Soc. 156 (1971), 419–454. MR 276418, DOI 10.1090/S0002-9947-1971-0276418-3
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
Ray A. Kunze, A note on square-integrable representations, J. Functional Analysis 6 (1970), 454–459. MR 0271749, DOI 10.1016/0022-1236(70)90072-8
Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Die Grundlehren der mathematischen Wissenschaften, Band 188, Springer-Verlag, New York-Heidelberg, 1972. MR 0498999