Symmetry of Weighted L1-Algebras and the GRS-Condition

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 Lω1(G) is a symmetric Banach *-algebra if and only if the weight function ω satisfies the GRS-condition. This condition...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2006-08, Vol.38 (4), p.625-635
Main Authors: Fendler, Gero, Gröchenig, Karlheinz, Leinert, Michael
Format: Article
Language:English
Online Access:Get full text
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Summary: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 Lω1(G) is a symmetric Banach *-algebra if and only if the weight function ω satisfies the GRS-condition. This condition expresses in a precise technical sense that ω grows subexponentially. 2000 Mathematics Subject Classification 43A20, 22D15, 22D12.
ISSN:0024-6093
1469-2120
DOI:10.1112/S0024609306018777