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On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups

Leszek Skrzypczak (1998)

Commentationes Mathematicae Universitatis Carolinae

In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.

On character amenable Banach algebras

Z. Hu, M. Sangani Monfared, T. Traynor (2009)

Studia Mathematica

We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...

On convolution operators with small support which are far from being convolution by a bounded measure

Edmond Granirer (1994)

Colloquium Mathematicae

Let C V p ( F ) be the left convolution operators on L p ( G ) with support included in F and M p ( F ) denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that C V p ( F ) , C V p ( F ) / M p ( F ) and C V p ( F ) / W are as big as they can be, namely have l as a quotient, where the ergodic space W contains, and at times is very big relative to M p ( F ) . Other subspaces of C V p ( F ) are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

Operator Figà-Talamanca-Herz algebras

Volker Runde (2003)

Studia Mathematica

Let G be a locally compact group. We use the canonical operator space structure on the spaces L p ( G ) for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues O A p ( G ) of the classical Figà-Talamanca-Herz algebras A p ( G ) . If p ∈ (1,∞) is arbitrary, then A p ( G ) O A p ( G ) and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that O A p ( G ) is a completely contractive Banach algebra for each p ∈ (1,∞), and that O A q ( G ) O A p ( G ) completely contractively for amenable...

Operator Segal algebras in Fourier algebras

Brian E. Forrest, Nico Spronk, Peter J. Wood (2007)

Studia Mathematica

Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator u u | H : S ¹ A ( G ) A ( H ) , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup, then the averaging...

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