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A note on Subalgebras of co-dimension 1

Published online by Cambridge University Press:  24 October 2008

J. F. Rennison
J. F. Rennison
Affiliation:
University of Kent at Canterbury
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Extract

Sawon and Warzecha established in (2) the general form of a subalgebra of codimension 1 in a commutative Banach algebra with identity. A short and elegant proof of their result was later given by Detraz in(1). This note is intended to show that an even more elementary proof is possible and which has the advantage that no use is made of the existence of maximal ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 673 - 674
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Detraz, J.Sous-algébres de codimension l et dérivations dans les algébres de Banach commutatives. Studia Math. 30 (1968), 79–82.CrossRefGoogle Scholar
(2)Sawon, Z. and Warzecha, A.On the general form of subalgebras of codimension l of B-algebras with a unit. Studia Math. 29 (1968), 249–260.CrossRefGoogle Scholar