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Banach algebras with one dimensional radical

Published online by Cambridge University Press:  17 April 2009

Lawrence Stedman
Lawrence Stedman
Affiliation:
Department of Mathematics, Faculty of Science, Australian National University, PO Box 4, Canberra, ACT 2600, Australia.
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Abstract

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A Banach algebra A with radical R is said to have property (S) if the natural mapping from the algebraic tensor product A ⊗ A onto A2 is open, when A ⊗ A is given the protective norm. The purpose of this note is to provide a counterexample to Zinde's claim that when A is commutative and R is one dimensional the fulfillment of property (S) in A implies its fulfillment in the quotient algebra A/R.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1983 , pp. 115 - 119
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Loy, Richard J., “The uniqueness of norm problem in Banach algebras with finite dimensional radical”, Automatic continuity and radical Banach algebras (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, to appear).Google Scholar
[2]Зинде, B.M. [ Zinde, V.M.], “Свойство ‘еднствености нормы’ для коммутативных Банаховых алсебр с конечномерным радикалом” [Unique norm property in commutative Banach algebras with finite-dimensional radicals], Vestnik Moskov. Univ. Ser. I Mat. Meh. (1970), No. 4, 3–8.Google ScholarPubMed