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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.
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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

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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