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The quasi-centre of a Banach algebra

Published online by Cambridge University Press:  24 October 2008

J. F. Rennison
J. F. Rennison
Affiliation:
Mathematical Institute, University of Kent, Canterbury
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Extract

An element a of a Banach algebra A over ࠶ will be called quasi-central if, for some K ≥ 1,

The set Q(A) of all quasi-central elements of A will be called the quasi-centre of A and the set of elements a which satisfy (1) for a particular value of K will be denoted by Q(K, A). The motivation for these definitions is the result of Le Page ([1], proposition 3) that Q(1, A) coincides with the centre Z(A) of A. The reader is referred to [2] and [3] for a study of the properties of quasi-central elements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 333 - 337
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Page, C. Le. Sur quelques conditions entraînant la commutativité dans les algèbres de Banach. C. R. Acad. Sci. Paris Sér. A-B 265 (1967), 235–237.Google Scholar
[2]Rennison, J. F.. Conditions related to centrality in a Banach algebra. J. London Math. Soc. 26, 2 (1982), 155–168.Google Scholar
[3]Rennison, J. F.. Conditions related to centrality in a Banach algebra. II. J. London Math. Soc. 35, (1987), 499–513.Google Scholar