Weak amenability of Banach algebras generated by some analytic semigroups

Galé, Jośe E.

doi:10.1090/S0002-9939-1988-0962826-X

Weak amenability of Banach algebras generated by some analytic semigroups
HTML articles powered by AMS MathViewer

by Jośe E. Galé PDF

Proc. Amer. Math. Soc. 104 (1988), 546-550 Request permission

Abstract:

In this paper it is shown that if $A$ is a Banach algebra generated by an analytic semigroup $({a^t})\operatorname {Re} t > 0$ such tnat $||{a^{1 + iy}}|| = O(|y{|^\rho }){\text { }}(y \in {\mathbf {R}})$, where $0 \leq \rho < 1/2$, then $A$ is weakly amenable, that is, each continuous derivation from $A$ to a commutative $A$-module is null.

References

Amenability and weak amenability for Beurling and Lipschitz algebras

Sobre condiciones de suficiencia para la propiedad tauberiana de Wiener

J. Esterle, Quasimultipliers, representations of $H^{\infty }$, and the closed ideal problem for commutative Banach algebras, Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981) Lecture Notes in Math., vol. 975, Springer, Berlin, 1983, pp. 66–162. MR 697579, DOI 10.1007/BFb0064548
J. Esterle and J. E. Galé, Regularity of Banach algebras generated by analytic semigroups satisfying some growth conditions, Proc. Amer. Math. Soc. 92 (1984), no. 3, 377–380. MR 759656, DOI 10.1090/S0002-9939-1984-0759656-7
B. E. Johnson, Continuity of centralisers on Banach algebras, J. London Math. Soc. 41 (1966), 639–640. MR 200741, DOI 10.1112/jlms/s1-41.1.639
Allan M. Sinclair, Continuous semigroups in Banach algebras, London Mathematical Society Lecture Note Series, vol. 63, Cambridge University Press, Cambridge-New York, 1982. MR 664431, DOI 10.1017/CBO9780511662423