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

Volker Runde

Studia Mathematica (1994)

  • Volume: 110, Issue: 1, page 97-104
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Runde, Volker. "When is there a discontinuous homomorphism from L¹(G)?." Studia Mathematica 110.1 (1994): 97-104. <http://eudml.org/doc/216101>.

@article{Runde1994,
abstract = {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.},
author = {Runde, Volker},
journal = {Studia Mathematica},
keywords = {automatic continuity; enveloping -algebra},
language = {eng},
number = {1},
pages = {97-104},
title = {When is there a discontinuous homomorphism from L¹(G)?},
url = {http://eudml.org/doc/216101},
volume = {110},
year = {1994},
}

TY - JOUR
AU - Runde, Volker
TI - When is there a discontinuous homomorphism from L¹(G)?
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 1
SP - 97
EP - 104
AB - 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.
LA - eng
KW - automatic continuity; enveloping -algebra
UR - http://eudml.org/doc/216101
ER -

References

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  1. [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. Zbl0518.46034
  2. [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. Zbl0497.43001
  3. [Bar2] B. A. Barnes, Ditkin's condition and [SIN]-groups, Monatsh. Math. 96 (1983), 1-15. Zbl0512.43002
  4. [B-L-Sch-V] J. Boidol, H. Leptin, J. Schürmann and D. Vahle, Räume primitiver Ideale von Gruppenalgebren, Math. Ann. 236 (1978), 1-13. Zbl0363.46057
  5. [B-D] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb. 80, Springer, 1973. 
  6. [Dal] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford Univ. Press, in preparation. 
  7. [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. Zbl0629.03030
  8. [G-M] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40. Zbl0219.22011
  9. [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. Zbl0529.43005
  10. [Hel] A. Ya. Helemskiĭ, The Homology of Banach and Topological Algebras, Math. Appl. (Soviet Ser.) 41, Kluwer, 1989 (translated from the Russian). 
  11. [Lau] K. B. Laursen, On discontinuous homomorphisms from L 1 ( G ) , Math. Scand. 30 (1972), 263-266. Zbl0244.46064
  12. [Pal] T. W. Palmer, Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741. Zbl0396.22001
  13. [Ped] G. K. Pedersen, C*-Algebras and their Automorphism Groups, London Math. Soc. Monographs 14, Academic Press, 1979. 
  14. [Run] V. Runde, Homomorphisms from L 1 ( G ) for G ∈ [FIA]¯ ∪ [Moore], J. Funct. Anal., to appear. 
  15. [Sin1] A. M. Sinclair, Homomorphisms from C*-algebras, Proc. London Math. Soc. (3) 29 (1974), 435-452. Zbl0293.46044
  16. [Sin2] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976. 

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