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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On weak containment properties

Author: Harald Rindler
Journal: Proc. Amer. Math. Soc. 114 (1992), 561-563
MSC: Primary 22D10; Secondary 43A65
MathSciNet review: 1057960
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Abstract: We prove, that two concepts of weak containment do not coincide, contradicting results in [1, Lemma 3.3 and Proposition 3.4]. The statement of Theorem 3.5 remains valid. There exist infinite tall compact groups $ G$ (i.e. the set $ \{ \sigma \in \hat G,\dim \sigma = n\} $ is finite for each positive integer $ n$) having the mean-zero weak containment property. Such groups do not have the dual Bohr approximation property or $ AP(\hat G) \ne C_\delta ^*(G)$.

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Keywords: Locally compact groups, left regular representation, amenable groups, Kazhdan's property $ T$, tall groups
Article copyright: © Copyright 1992 American Mathematical Society