Weighted group algebra as an ideal in its second dual space

Author:
F. Ghahramani

Journal:
Proc. Amer. Math. Soc. **90** (1984), 71-76

MSC:
Primary 43A22; Secondary 43A15, 46J99, 47B99

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722417-9

MathSciNet review:
722417

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Abstract | References | Similar Articles | Additional Information

Abstract: For a locally compact group let be a weighted group algebra. We characterize compact and weakly compact multipliers on . This characterization is employed to find a necessary and sufficient condition for to be an ideal in its second dual space, where the second dual is equipped with an Arens product. In the special case where , we deduce a result due to K. P. Wong that if is a compact group, then is an ideal in its second dual space and its converse due to S. Watanabe.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722417-9

Keywords:
Weighted group algebra,
compact multiplier,
Arens product

Article copyright:
© Copyright 1984
American Mathematical Society