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Factorization and bounded approximate identities for a class of convolution Banach algebras

Published online by Cambridge University Press:  18 May 2009

S. I. Ouzomgi
S. I. Ouzomgi
Affiliation:
Department of Mathematics and Computer Science, California State University, Long Beach, Long Beach, California90840
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An algebra A factors if, for each a ∈ A, there exist b, c ∈ A with a = bc. A bounded approximate identity for a Banach algebra A is a net (eα) ⊂ A such that aeα → a and eαa → a for each a ∈ A and such that sup ‖eα ‖ < ∞. It is well known [2, 11.10] that if A has a bounded approximate identity, then A factors. But a Banach algebra may factor even if it does not have a bounded approximate identity: an example which is non-commutative and separable, and an example which is commutative and nonseparable, are given in [3, §22]. However, we do not know an example of a commutative, separable Banach algebra which factors, but which does not have a bounded approximate identity. See 4 for related work.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 211 - 214
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

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