Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T12:58:54.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuity of homomorphisms and derivations from algebras of approximable and nuclear operators

Published online by Cambridge University Press:  24 October 2008

H. G. Dales  and
H. Jarchow
H. G. Dales
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
H. Jarchow
Affiliation:
Mathematisches Institut, Universität Zurich, Rämistrasse 74, Zurich CH-8001, Switzerland
Get access Rights & Permissions [Opens in a new window]

Extract

1. Let be a Banach algebra. We say that homomorphisms from are continuous if every homomorphism from into a Banach algebra is automatically continuous, and that derivations from are continuous if every derivation from into a Banach -bimodule is automatically continuous.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 465 - 473
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bade, W. G. and Curtis, P. C. Jr., Homomorphisms of commutative Banach algebras. American J. Math. 82 (1960), 589–608.CrossRefGoogle Scholar
[2]Bade, W. G. and Curtis, P. C. Jr., Prime ideals and automatic continuity problems for Banach algebras. J. Fund. Analysis 29 (1978), 88–103.CrossRefGoogle Scholar
[3]Bonsall, F. F. and Duncan, J.. Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
[4]Dales, H. G.. The uniqueness of the functional calculus. Proc. London Math. Soc. (3), 27 (1973), 638–648.CrossRefGoogle Scholar
[5]Dales, H. G.. A discontinuous homomorphism from C(X). Amer. J.Math. 101 (1976), 647–734.CrossRefGoogle Scholar
[6]Dales, H. G., Loy, R. J. and Willis, G. A.. Homomorphisms and derivations from (E). J. Fund. Analysis 120 (1994), 201–219.CrossRefGoogle Scholar
[7]Dixon, P. G.. Left approximate identities in algebras of compact operators on Banach spaces. Proc. Royal Soc. of Edinburgh 104 A (1986), 169–175.CrossRefGoogle Scholar
[8]Esterle, J. R.. Injection de semi-groupes divisibles dans des algèbres de convolution et construction d'homomorphismes discontinus de C(K). Proc. London Math. Soc. (3), 36 (1978), 46–58.CrossRefGoogle Scholar
[9]Grothendieck, A.. The trace of certain operators. Studia Math. 20 (1961), 141–143.CrossRefGoogle Scholar
[10]Jameson, G. J. O.. Summing and nuclear norms in Banach space theory. London Mathematical Society Student Texts (Cambridge University Press, 1987).Google Scholar
[11]Johnson, B. E.. Continuity of homomorphisms of algebras of operators. J. London Math. Soc. 40 (1967), 537–541.CrossRefGoogle Scholar
[12]Johnson, W. B., König, H., Maurey, B. and Retherford, J. R.. Eigenvalues of p-summing and l p-type operators in Banach spaces. J. Funct. Analysis 32 (1979), 353–380.CrossRefGoogle Scholar
[13]Jarchow, H. and Ott, R.. On trace ideals. Math. Nachr. 108 (1982), 23–37.CrossRefGoogle Scholar
[14]Konig, H.. Eigenvalue distribution of compact operators (Birkhauser, 1986).CrossRefGoogle Scholar
[15]Lindenstrauss, J. and Tzafriri, L.. Classical Banach spaces I (Berlin, 1977).CrossRefGoogle Scholar
[16]Pietsch, A.. Operator ideals (North Holland, 1980).Google Scholar
[17]Pietsch, A.. Eigenvalues and s-Numbers. Cambridge Studies in Advanced Mathematics (Cambridge University Press, 1986).Google Scholar
[18]Pisier, G.. Counterexamples to a conjecture of Grothendieck. Acta. Math. 151 (1983), 181–208.CrossRefGoogle Scholar
[19]Pisier, G.. Factorization of linear operators and geometry of Banach spaces. American Math. Soc. Regional Conference Series in Mathematics 60 (1986).CrossRefGoogle Scholar
[20]Read, C.. Discontinuous derivations on the algebra of bounded operators on a Banach space. J. London Math. Soc. (2) 40 (1989), 305–326.CrossRefGoogle Scholar
[21]Selivanov, Yu. V.. Homological characterizations of the approximation property for Banach spaces. Glasgow Math. J. 34 (1992), 229–239.CrossRefGoogle Scholar