Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.
@article{bwmeta1.element.bwnjournal-article-smv125i1p75bwm, author = {Fr\'ed\'eric Gourdeau}, title = {Amenability and the second dual of a Banach algebra}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {75-81}, zbl = {0907.46040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p75bwm} }
Gourdeau, Frédéric. Amenability and the second dual of a Banach algebra. Studia Mathematica, Tome 122 (1997) pp. 75-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p75bwm/
[00000] [1] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848. | Zbl 0044.32601
[00001] [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973. | Zbl 0271.46039
[00002] [3] I. G. Craw and N. J. Young, Regularity of multiplication in weighted group and semigroup algebras, Quart. J. Math. Oxford Ser. (2) 25 (1974), 351-358. | Zbl 0304.46027
[00003] [4] F. Ghahramani, R. Loy and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc., to appear. | Zbl 0851.46035
[00004] [5] F. Gourdeau, Amenability of Banach algebras, Ph.D. Thesis, University of Cambridge, 1989. | Zbl 0717.46042
[00005] [6] F. Gourdeau, Amenability of Lipschitz algebras, Math. Proc. Cambridge Philos. Soc. 112 (1992), 581-588. | Zbl 0782.46043
[00006] [7] N. Grønbæk, Amenability of weighted discrete convolution algebras on cancellative semigroups, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 351-360. | Zbl 0678.46038
[00007] [8] N. Grønbæk, A characterization of weak amenability, Studia Math. 94 (1989), 149-162.
[00008] [9] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). | Zbl 0256.18014
[00009] [10] N. J. Young, The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. (2) 24 (1973), 59-62. | Zbl 0252.43009