Hyper-Tauberian algebras and weak amenability of Figà-Talamanca-Herz algebras |
| |
Authors: | Ebrahim Samei |
| |
Institution: | Department of Mathematics, University of Manitoba, Winnipeg, Man., Canada R3T 2N2 |
| |
Abstract: | We study certain commutative regular semisimple Banach algebras which we call hyper-Tauberian algebras. We first show that they form a subclass of weakly amenable Tauberian algebras. Then we investigate the basic and hereditary properties of them. Moreover, we show that if A is a hyper-Tauberian algebra, then the linear space of bounded derivations from A into any Banach A-bimodule is reflexive. We apply these results to the Figà-Talamanca-Herz algebra Ap(G) of a locally compact group G for p∈(1,∞). We show that Ap(G) is hyper-Tauberian if the principal component of G is abelian. Finally, by considering the quantization of these results, we show that for any locally compact group G, Ap(G), equipped with an appropriate operator space structure, is a quantized hyper-Tauberian algebra. This, in particular, implies that Ap(G) is operator weakly amenable. |
| |
Keywords: | Tauberian algebra Local operators Approximately local derivations Locally compact groups Fourier algebra Figà -Talamanca-Herz algebra Operator spaces Weak amenability |
本文献已被 ScienceDirect 等数据库收录! |
|