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Transactions of the American Mathematical Society

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Amenability of weighted convolution algebras on locally compact groups


Author: Niels Grønbæk
Journal: Trans. Amer. Math. Soc. 319 (1990), 765-775
MSC: Primary 43A20
DOI: https://doi.org/10.1090/S0002-9947-1990-0962282-5
MathSciNet review: 962282
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Abstract: We give a direct transition from the existence of a bounded right approximate identity in the diagonal ideal for a weighted convolution algebra on a locally compact group to the existence of translation invariant means on an associated weighted $ {L^\infty }$-space, thus giving a characterization of amenability for such an algebra.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0962282-5
Keywords: Amenable, bounded approximate identity, convolution, diagonal ideal, translation invariant mean
Article copyright: © Copyright 1990 American Mathematical Society