Amenability and the second dual of a Banach algebra

• Autorzy: Frédéric Gourdeau
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

amenability; Arens regularity; second dual

Kategorie tematyczne

• 46H20: Structure, classification of topological algebras
• 43A20: L 1 -algebras on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 1
• Strony: 75-81

Daty

wydano

1997

otrzymano

1996-09-11

Twórcy

autor

Frédéric Gourdeau

• Département de mathématiques et de statistique, Université Laval, Cité Universitaire, Québec, Canada G1K 7P4

Bibliografia

• [1] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
• [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973.
• [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.
• [4] F. Ghahramani, R. Loy and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc., to appear.
• [5] F. Gourdeau, Amenability of Banach algebras, Ph.D. Thesis, University of Cambridge, 1989.
• [6] F. Gourdeau, Amenability of Lipschitz algebras, Math. Proc. Cambridge Philos. Soc. 112 (1992), 581-588.
• [7] N. Grønbæk, Amenability of weighted discrete convolution algebras on cancellative semigroups, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 351-360.
• [8] N. Grønbæk, A characterization of weak amenability, Studia Math. 94 (1989), 149-162.
• [9] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
• [10] N. J. Young, The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. (2) 24 (1973), 59-62.