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1994 | 110 | 1 | 97-104
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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.
Słowa kluczowe
  • Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany
  • [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.
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  • [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.
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  • [Run] V. Runde, Homomorphisms from $L^1(G)$ for G ∈ [FIA]¯ ∪ [Moore], J. Funct. Anal., to appear.
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