On convolution dominated operators
| Autor: | Gero Fendler, Michael Leinert |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete group
Star (game theory) 47B35 43A20 01 natural sciences Bounded operator 510 Mathematics Symmetric group 0103 physical sciences FOS: Mathematics 0101 mathematics Operator Algebras (math.OA) Mathematics symmetry Discrete mathematics Algebra and Number Theory Group (mathematics) 010102 general mathematics Subalgebra inverse-closed subalgebras Mathematics - Operator Algebras Locally compact group Functional Analysis (math.FA) Mathematics - Functional Analysis Bounded function 010307 mathematical physics Convolution dominated operators Analysis |
| DOI: | 10.11588/heidok.00029231 |
| Popis: | For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in L^2(G)$ $ |Af(x)| \leq a * |f| (x)$, for almost all $x \in G$. In the case of discrete groups those operators can be dealt with quite sufficiently if the group in question is rigidly symmetric. For non-discrete groups we investigate the subalgebra of regular convolution dominated operators $CD_{reg}(G)$. For amenable $G$ which is rigidly symmetric as a discrete group, we show that any element of $CD_{reg}(G)$ is invertible in $CD_{reg}(G)$ if it is invertible as a bounded operator on $L^2(G)$. We give an example of a symmetric group $E$ for which the convolution dominated operators are not inverse-closed in the bounded operators on $L^2(E)$. 22pages, to appear in Integral Equations and Operator Theory |
| Databáze: | OpenAIRE |
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