Locally compact groups which have the weakly compact homomorphism property

Runde, Volker

doi:10.1090/S0002-9939-1995-1273521-8

Locally compact groups which have the weakly compact homomorphism property
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by Volker Runde PDF

Proc. Amer. Math. Soc. 123 (1995), 3363-3364 Request permission

Abstract:

A locally compact group G is WCHP if every weakly compact homomorphism from ${L^1}(G)$ into a Banach algebra has finite-dimensional range, and is ${\text {WCHP}^ + }$ if every extension of G by an abelian group is WCHP. We verify the ${\text {WCHP}^ + }$ property for certain locally compact groups, including all Moore groups and all connected groups.

References

Siegfried Grosser and Martin Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1–40. MR 284541, DOI 10.1515/crll.1971.246.1
B. E. Johnson, Weakly compact homomorphisms from group algebras, Proc. Amer. Math. Soc. 119 (1993), no. 4, 1249–1258. MR 1158001, DOI 10.1090/S0002-9939-1993-1158001-0
Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
T. W. Palmer, Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), no. 4, 683–741. MR 513952, DOI 10.1216/RMJ-1978-8-4-683
Lewis C. Robertson, A note on the structure of Moore groups, Bull. Amer. Math. Soc. 75 (1969), 594–599. MR 245721, DOI 10.1090/S0002-9904-1969-12252-4
George Willis, The continuity of derivations from group algebras: factorizable and connected groups, J. Austral. Math. Soc. Ser. A 52 (1992), no. 2, 185–204. MR 1143188, DOI 10.1017/S1446788700034340