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1994 | 110 | 1 | 97-104
Tytuł artykułu

When is there a discontinuous homomorphism from L¹(G)?

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Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.
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autor
  • Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany, runde@math.uni-sb.de
Bibliografia
  • [A-D] E. Albrecht and H. G. Dales, Continuity of homomorphisms from C*-algebras and other Banach algebras, in: J. M. Bachar, W. G. Bade, P. C. Curtis Jr., H. G. Dales and M. P. Thomas (eds.), Radical Banach Algebras and Automatic Continuity, Lecture Notes in Math. 975, Springer, 1983, 375-396.
  • [Bar1] B. A. Barnes, Ideal and representation theory of the $L^1$-algebra of a group with polynomial growth, Colloq. Math. 45 (1981), 301-315.
  • [Bar2] B. A. Barnes, Ditkin's condition and [SIN]-groups, Monatsh. Math. 96 (1983), 1-15.
  • [B-L-Sch-V] J. Boidol, H. Leptin, J. Schürmann and D. Vahle, Räume primitiver Ideale von Gruppenalgebren, Math. Ann. 236 (1978), 1-13.
  • [B-D] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb. 80, Springer, 1973.
  • [Dal] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford Univ. Press, in preparation.
  • [D-W] H. G. Dales and W. H. Woodin, An Introduction to Independence for Analysts, London Math. Soc. Lecture Note Ser. 115, Cambridge Univ. Press, 1987.
  • [G-M] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40.
  • [H-K-K] W. Hauenschild, E. Kaniuth and A. Kumar, Ideal structure of Beurling algebras on [FC]¯-groups, J. Funct. Anal. 51 (1983) 213-228.
  • [Hel] A. Ya. Helemskiĭ, The Homology of Banach and Topological Algebras, Math. Appl. (Soviet Ser.) 41, Kluwer, 1989 (translated from the Russian).
  • [Lau] K. B. Laursen, On discontinuous homomorphisms from $L^1(G)$, Math. Scand. 30 (1972), 263-266.
  • [Pal] T. W. Palmer, Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741.
  • [Ped] G. K. Pedersen, C*-Algebras and their Automorphism Groups, London Math. Soc. Monographs 14, Academic Press, 1979.
  • [Run] V. Runde, Homomorphisms from $L^1(G)$ for G ∈ [FIA]¯ ∪ [Moore], J. Funct. Anal., to appear.
  • [Sin1] A. M. Sinclair, Homomorphisms from C*-algebras, Proc. London Math. Soc. (3) 29 (1974), 435-452.
  • [Sin2] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976.
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bwmeta1.element.bwnjournal-article-smv110i1p97bwm
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