Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inner amenable locally compact groups


Authors: Anthony To Ming Lau and Alan L. T. Paterson
Journal: Trans. Amer. Math. Soc. 325 (1991), 155-169
MSC: Primary 43A07
MathSciNet review: 1010885
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the relationship between amenability, inner amenability and property $ P$ of a von Neumann algebra. We give necessary conditions on a locally compact group $ G$ to have an inner invariant mean $ m$ such that $ m(V) = 0$ for some compact neighborhood $ V$ of $ G$ invariant under the inner automorphisms. We also give a sufficient condition on $ G$ (satisfied by the free group on two generators or an I.C.C. discrete group with Kazhdan's property $ T$, e.g., $ {\text{SL}}(n,\mathbb{Z})$, $ n \geq 3$) such that each linear form on $ {L^2}(G)$ which is invariant under the inner automorphisms is continuous. A characterization of inner amenability in terms of a fixed point property for left Banach $ G$-modules is also obtained.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A07

Retrieve articles in all journals with MSC: 43A07


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1010885-5
PII: S 0002-9947(1991)1010885-5
Keywords: Amenable locally compact groups, inner amenable groups, $ [{\text{IN}}]$-groups, property $ P$, von Neumann algebra, free group, Kazhdan's property $ T$, automatic continuity, fixed point property
Article copyright: © Copyright 1991 American Mathematical Society