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Ditkin's condition for certain Beurling algebras |
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| Authors: | Sen-Zhong Huang Jan van Neerven Frank Rä biger |
| Affiliation: | Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany ; Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany ; Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, F. R. Germany |
| Abstract: | Let  be a locally compact abelian group. A function  is said to be a weight if it is locally bounded, Borel measurable and submultiplicative. We call a weight  on  semi-bounded if there exist a constant  and a subsemigroup  with  such that
for all |
| Keywords: | Ditkin's condition group representation spectrum |
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Using functional analytic methods, we show that all Beurling algebras 
whose defining weight 
is semi-bounded satisfy Ditkin's condition.