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SYMMETRY OF WEIGHTED $L{\uppercase{\footnotesize{L^1}}}$-ALGEBRAS AND THE GRS-CONDITION

Published online by Cambridge University Press:  24 July 2006

GERO FENDLER ,
KARLHEINZ GRÖCHENIG  and
MICHAEL LEINERT
GERO FENDLER
Affiliation:
Finstertal 16, D-69514 Laudenbach, Germanygero.fendler@t-online.de
KARLHEINZ GRÖCHENIG
Affiliation:
GSF – National Research Center for Environmental and Health, Institute of Biomathematics and Biometry, Ingolstädter Str. 1, D-85764 Neuherberg, Germanykarlheinz.groechenig@gsf.de Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austriakarlheinz-groechenig@univie.ac.at
MICHAEL LEINERT
Affiliation:
Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germanyleinert@math.uni-heidelberg.de
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Abstract

Let $G$ be a compactly generated, locally compact group of polynomial growth. Removing a restrictive technical condition from a previous work, we show that the weighted group algebra $L^{1}_{\omega}(G)$ is a symmetric Banach $*$-algebra if and only if the weight function $\omega $ satisfies the GRS-condition. This condition expresses in a precise technical sense that $\omega $ grows subexponentially.

Keywords

43A2022D1522D12
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 4 , August 2006 , pp. 625 - 635
Copyright
The London Mathematical Society 2006

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