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A Note on L-sets

Gero Fendler — 2002

Colloquium Mathematicae

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 L p -version of a theorem of D.A. Raikov

Gero Fendler — 1985

Annales de l'institut Fourier

Let G be a locally compact group, for p ( 1 , ) let P f p ( G ) denote the closure of L 1 ( G ) in the convolution operators on L p ( G ) . Denote W p ( G ) the dual of P f p ( G ) which is contained in the space of pointwise multipliers of the Figa-Talamanca Herz space A p ( G ) . It is shown that on the unit sphere of W p ( G ) the σ ( W p , P f p ) topology and the strong A p -multiplier topology coincide.

A note on certain partial sum operators

Marek BożejkoGero Fendler — 2006

Banach Center Publications

We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of L p 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 L p 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

Gero FendlerKarlheinz GröchenigMichael Leinert — 2010

Banach Center Publications

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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