Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T12:09:19.261Z Has data issue: false hasContentIssue false
  • English
  • Français

Rank one elements of Banach algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  26 February 2010

J. A. Erdos ,
S. Giotopoulos  and
M. S. Lambrou
J. A. Erdos
Affiliation:
King's College, London WC2R 2LS.
S. Giotopoulos
Affiliation:
King's College, London WC2R 2LS.
M. S. Lambrou
Affiliation:
King's College, London WC2R 2LS.
Get access

Extract

The question, whether a given element of a C*-algebra has an image of rank one in some faithful representation, was studied in [3]. Such elements were characterised there by the property of being “single” (as defined below). As was pointed out in [3], Section 5, this criterion fails for general Banach algebras and the purpose of this paper is to provide a stronger condition giving the required representation property for any semi-simple Banach algebra.

MSC classification

Secondary: 46H15: Representations of topological algebras
Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 178 - 181
Copyright
Copyright © University College London 1977

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

1.Alexander, J. C.. “Compact Banach algebras”, Proc. London Math. Soc., (3), 18 (1968), 1–19.CrossRefGoogle Scholar
2.Bonsall, F. F. and Duncan, J.. Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
3.Erdos, J. A.. “On certain elements of C*-algebras”, Illinois J. Math., 15 (1971), 682–693.CrossRefGoogle Scholar