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Proceedings of the American Mathematical Society

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Locally compact groups which have the weakly compact homomorphism property


Author: Volker Runde
Journal: Proc. Amer. Math. Soc. 123 (1995), 3363-3364
MSC: Primary 22D05; Secondary 22D15, 22D20
DOI: https://doi.org/10.1090/S0002-9939-1995-1273521-8
MathSciNet review: 1273521
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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 [Enhancements On Off] (What's this?)

  • [G-M] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40. MR 0284541 (44:1766)
  • [Joh] B. E. Johnson, Weakly compact homomorphisms from group algebras, Proc. Amer. Math. Soc. 119 (1993), 1249-1258. MR 1158001 (94a:43004)
  • [M-Z] D. Montgomery and L. Zippin, Topological transformation groups, Interscience, New York, 1955. MR 0073104 (17:383b)
  • [Pal] T. W. Palmer, Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), 682-741. MR 513952 (81j:22003)
  • [Rob] L. C. Robertson, A note on the structure of Moore groups, Bull. Amer. Math. Soc. 75 (1969), 594-599. MR 0245721 (39:7027)
  • [Wil] G. A. Willis, The continuity of derivations from group algebras: Factorizable and connected groups, J. Austral. Math. Soc. Ser. A 52 (1992), 185-204. MR 1143188 (93b:46096)

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DOI: https://doi.org/10.1090/S0002-9939-1995-1273521-8
Article copyright: © Copyright 1995 American Mathematical Society

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