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

Content Provider	Scilit
Author	Ouzomgi, S. I.
Copyright Year	1986
Description	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 $(e_{α}$) ⊂ A such that $ae_{α}$ → a and $e_{α}$a → a for each a ∈ A and such that sup $‖e_{α}$ ‖ < ∞. 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.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/299AE290B282C5FBB05D13E0BFC81F3D/S0017089500006522a.pdf/div-class-title-factorization-and-bounded-approximate-identities-for-a-class-of-convolution-banach-algebras-div.pdf
Ending Page	214
Page Count	4
Starting Page	211
ISSN	00170895
e-ISSN	1469509X
DOI	10.1017/s0017089500006522
Journal	Glasgow Mathematical Journal
Issue Number	2
Volume Number	28
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1986-07-01
Access Restriction	Open
Subject Keyword	Glasgow Mathematical Journal Approximate Identity Bounded Approximate
Content Type	Text
Resource Type	Article
Subject	Mathematics