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Banach Center Publications

2010 | 89 | 1 | 121-127

Convolution-dominated integral operators

EN

Abstrakty

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.

121-127

wydano
2010

Twórcy

autor
• Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
autor
• Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
autor
• Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany