An extension property for the Figà-Talamanca Herz algebra
نویسندگان
چکیده
منابع مشابه
Operator Figà-Talamanca–Herz algebras
Let G be a locally compact group. We use the canonical operator space structure on the spaces L(G) for p ∈ [1,∞] introduced by G. Pisier to define operator space analoguesOAp(G) of the classical Figà-Talamanca–Herz algebrasAp(G). If p ∈ (1,∞) is arbitrary, then Ap(G) ⊂ OAp(G) such that the inclusion is a contraction; if p = 2, then OA2(G) ∼= A(G) as Banach spaces spaces, but not necessarily as ...
متن کاملOperator space structure and amenability for Figà-Talamanca–Herz algebras
Column and row operator spaces — which we denote by COL and ROW, respectively — over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p, p ∈ (1,∞) with 1 p + 1 p = 1, we use the operator space structure on CB(COL(L ′ (G))) to equip the Figà-Talamanca–Herz algebra Ap(G) with ...
متن کاملFourier and Figà-Talamanca–Herz algebras on amenable, locally compact groups
For a locally compact group G, let A(G) denote its Fourier algebra and, for p ∈ (1,∞), let Ap(G) be the corresponding Figà-Talamanca–Herz algebra. For amenable G and p, p ∈ (1,∞) such that 1 p + 1 p , we show that Ap(G) ∩Ap′(G) = A(G).
متن کاملp-Operator Spaces and Figà-Talamanca-Herz Algebras
We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact g...
متن کاملRepresentations of locally compact groups on QSLp-spaces and a p-analog of the Fourier–Stieltjes algebra
For a locally compact group G and p ∈ (1,∞), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of Lp spaces. For p = 2, this is the usual Fourier–Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figà-Talamanca–Herz algebra Ap(G). If 2 ≤ q ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09679-2