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

Studia Mathematica (1994)

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

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topRunde, 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

top- [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
- [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
- [Bar2] B. A. Barnes, Ditkin's condition and [SIN]-groups, Monatsh. Math. 96 (1983), 1-15. Zbl0512.43002
- [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
- [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. Zbl0629.03030
- [G-M] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40. Zbl0219.22011
- [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
- [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 ${L}^{1}\left(G\right)$, Math. Scand. 30 (1972), 263-266. Zbl0244.46064
- [Pal] T. W. Palmer, Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741. Zbl0396.22001
- [Ped] G. K. Pedersen, C*-Algebras and their Automorphism Groups, London Math. Soc. Monographs 14, Academic Press, 1979.
- [Run] V. Runde, Homomorphisms from ${L}^{1}\left(G\right)$ 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. Zbl0293.46044
- [Sin2] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976.

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