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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak amenability of Banach algebras generated by some analytic semigroups


Author: Jośe E. Galé
Journal: Proc. Amer. Math. Soc. 104 (1988), 546-550
MSC: Primary 46J35; Secondary 46H25
MathSciNet review: 962826
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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 $ \vert\vert{a^{1 + iy}}\vert\vert = O(\vert y{\vert^\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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0962826-X
Keywords: Banach algebra, Weak amenability, analytic semigroup
Article copyright: © Copyright 1988 American Mathematical Society