Geodesic
Factorization and bounded approximate identities for a class of convolution Banach algebras
Glasgow mathematical journal, Tome 28 (1986) no. 2, pp. 211-214

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Ouzomgi, S. I. Factorization and bounded approximate identities for a class of convolution Banach algebras. Glasgow mathematical journal, Tome 28 (1986) no. 2, pp. 211-214. doi: 10.1017/S0017089500006522
@article{10_1017_S0017089500006522,
     author = {Ouzomgi, S. I.},
     title = {Factorization and bounded approximate identities for a class of convolution {Banach} algebras},
     journal = {Glasgow mathematical journal},
     pages = {211--214},
     year = {1986},
     volume = {28},
     number = {2},
     doi = {10.1017/S0017089500006522},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006522/}
}
TY  - JOUR
AU  - Ouzomgi, S. I.
TI  - Factorization and bounded approximate identities for a class of convolution Banach algebras
JO  - Glasgow mathematical journal
PY  - 1986
SP  - 211
EP  - 214
VL  - 28
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006522/
DO  - 10.1017/S0017089500006522
ID  - 10_1017_S0017089500006522
ER  - 
%0 Journal Article
%A Ouzomgi, S. I.
%T Factorization and bounded approximate identities for a class of convolution Banach algebras
%J Glasgow mathematical journal
%D 1986
%P 211-214
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006522/
%R 10.1017/S0017089500006522
%F 10_1017_S0017089500006522

[1] 1.Bade, W. G. and Dales, H. G., Norms and ideals in radical convolution algebras. J. Fund. Anal. 41 (1981), 77–109. Google Scholar | DOI

[2] 2.Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer, 1973). Google Scholar | DOI

[3] 3.Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules, Lecture Notes in Mathematics 768 (Springer, 1979). Google Scholar | DOI

[4] 4.Ouzomgi, S. I., Factorization and automatic continuity for an algebra of infinitely differentiate functions, J. London Math. Soc. (2) 30 (1984), 265–280. Google Scholar | DOI

Cité par Sources :