Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1992-1057960-3
MathSciNet review: 1057960
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)

  • [1] C. Chou, Almost periodic operators in $ VN(G)$, Trans. Amer. Math. Soc. 317 (1990), 229-253. MR 943301 (90d:43004)
  • [2] M. F. Hutchison, Tall profinite groups, Bull. Austral. Math. Soc. 18 (1978), 421-428. MR 508813 (80h:20044)
  • [3] H. Rindler, Groups of measure preserving transformations. II, Math. Z. 199 (1988), 581-588. MR 968324 (90a:28024)
  • [4] J. Rosenblatt, Translation-invariant linear forms on $ {L_p}(G)$, Proc. Amer. Math. Soc. 94 (1985), 226-228. MR 784168 (86e:43006)
  • [5] K. Schmidt, Amenability, Kazhdan's property $ T$, strong ergodicity and invariant means for ergodic group actions, Ergodic Theory Dynamical Systems 1 (1981), 223-236. MR 661821 (83m:43001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22D10, 43A65

Retrieve articles in all journals with MSC: 22D10, 43A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1057960-3
Keywords: Locally compact groups, left regular representation, amenable groups, Kazhdan's property $ T$, tall groups
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society