BIBCYT Autor: Alejandría BE 7.0.7b0

Autor: =Miao , Tianxuan

Sólo un registro cumplió la condición especificada en la base de información BIBCYT.

Autor:	Miao , Tianxuan
Título:	Approximation properties and approximate identities of Ap(G)
Páginas/Colación:	pp. 1581-1595
Fecha:	March 2009

Transactions of the American Mathematical Society Vol. 361, no.3 March 2009

Información de existencia

Palabras Claves:

AMENABLE GROUPS,

APPROXIMATE IDENTITY,

APPROXIMATION PROPERTY,

HERZ ALGEBRA,

MULTIPLIER ALGEBRA

Resumen
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For a locally compact group and $1 < p < \infty$ , let $A_{p}(G)$ be the Figà-Talamanca-Herz algebra. Then the multiplier algebra $MA_{p}(G)$ of $A_{p}(G)$ is a dual space. We say that $A_{p}(G)$ has the approximation property (or simply, AP) in $MA_{p}(G)$ if there is a net $\{ u_{\alpha } \}$ in $A_{p}(G)$ such that $u_{\alpha }\rightarrow 1$ in the associated $weak^{*}$ topology. We prove that $A_{p}(G)$ has the AP in $MA_{p}(G)$ if and only if there exists a net $\{ a_{\alpha } \}$ in $A_{p}(G)$ such that $\Vert a_{\alpha } a - a\Vert_{A_{p}(G)}\rightarrow 0$ uniformly for in any compact subset of $A_{p}(G)$ . Consequently, we have that if $A_{p}(G)$ has the AP in $MA_{p}(G)$ , then $A_{p}(G)$ has the approximation property as a Banach space in the sense of Grothendieck for a discrete group . We also study the relationship between the AP of $A_{p}(G)$ in $MA_{p}(G)$ and the weak amenability of .

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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