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A Note on L-sets

100%
Fendler G.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 2
281-284
EN
Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.
2
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A note on certain partial sum operators

63%
Bożejko M., Fendler G.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
117-225
EN
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.
3
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Convolution-dominated integral operators

51%
Fendler G., Gröchenig K., Leinert M.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
121-127
EN
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 \cite{fgl08a, fgl08}. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where the products are restricted to those given by multiplication with left uniformly continuous functions. This algebra, $CD_{reg}(G)$, is canonically isomorphic to a twisted L¹-algebra. For amenable G that is rigidly symmetric as a discrete group we show the following result: An element of $CD_{reg}(G)$ is invertible in $CD_{reg}(G)$ if and only if it is invertible as a bounded operator on L²(G). This report is about work in progress. Complete details and further results will be given in a paper still in preparation.
4
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A uniformly bounded representation associated to a free set in a discrete group

50%
Fendler G.
Colloquium Mathematicum
|
1990
|
tom 59
|
nr 2
223-229
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