A uniformly bounded representation associated to a free set in a discrete group
A Note on L-sets
Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.
An -version of a theorem of D.A. Raikov
Let be a locally compact group, for let denote the closure of in the convolution operators on . Denote the dual of which is contained in the space of pointwise multipliers of the Figa-Talamanca Herz space . It is shown that on the unit sphere of the topology and the strong -multiplier topology coincide.
Variants of Littlewood-Paley theory.
On Representations in Banach Spaces.
A note on certain partial sum operators
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
Convolution-dominated integral operators
For a locally compact group G we consider the algebra CD(G) of convolution-dominated operators on L²(G), where an operator A: L²(G) → L²(G) is called convolution-dominated if there exists a ∈ L¹(G) such that for all f ∈ L²(G) |Af(x)| ≤ a⋆|f|(x), for almost all x ∈ G. (1) The case of discrete groups was treated in previous publications [, ]. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where the products...
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