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Symmetry of Weighted L 1 ‐Algebras and the GRS‐Condition
Author(s) -
Fendler Gero,
Gröchenig Karlheinz,
Leinert Michael
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018777
Subject(s) - mathematics , polynomial , mathematics subject classification , symmetry (geometry) , weight function , pure mathematics , banach algebra , function (biology) , algebra over a field , banach space , mathematical analysis , geometry , evolutionary biology , biology
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 algebraL ω 1 ( 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.