scholarly journals A characterization of the identity operator on $L^\infty$-spaces and its application to locally compact groups

1981 ◽  
Vol 21 (2) ◽  
pp. 301-317
Author(s):  
Tôru Umeda
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Identity Operator ◽  
Locally Compact

scholarly journals A Note on Amenability of Locally Compact Quantum Groups

2014 ◽  
Vol 57 (2) ◽  
pp. 424-430 ◽  
Author(s):  
Piotr M. Sołtan ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Short Note ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups

AbstractIn this short note we introduce a notion called quantum injectivity of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. In particular, this provides a new characterization of amenability of locally compact groups.

Characterization of non-compact locally compact groups by cocompact subgroups

2020 ◽  
Vol 23 (1) ◽  
pp. 17-24
Author(s):  
Bilel Kadri
Keyword(s):  
Topological Group ◽  
Finite Index ◽  
Quotient Space ◽  
Open Subgroup ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

AbstractA subgroup H of a topological group G is called cocompact (or uniform) if the quotient space {G/\overline{H}} is compact, where {\overline{H}} denotes the closure of H in G. The purpose of this paper is to give a characterization of non-compact locally compact groups with the property that every non-trivial closed (respectively, open) subgroup is cocompact (respectively, has finite index).

A cohomological characterization of amenable actions

1991 ◽  
Vol 110 (3) ◽  
pp. 491-504
Author(s):  
C. Anantharaman-Delaroche
Keyword(s):  
Dynamical Systems ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Classical Characterization

AbstractWe give a new characterization of amenability for dynamical systems, in cohomological terms, which generalizes the classical characterization of amenable locally compact groups stated by Johnson.

LOCALLY COMPACT GROUPS ADMITTING FAITHFUL STRONGLY CHAOTIC ACTIONS ON HAUSDORFF SPACES

2013 ◽  
Vol 23 (09) ◽  
pp. 1350158 ◽  
Author(s):  
FRIEDRICH MARTIN SCHNEIDER ◽  
SEBASTIAN KERKHOFF ◽  
MIKE BEHRISCH ◽  
STEFAN SIEGMUND
Keyword(s):  
Hausdorff Space ◽  
Geometric Characterization ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Action

In this paper we provide a geometric characterization of those locally compact Hausdorff topological groups which admit a faithful strongly chaotic continuous action on some Hausdorff space.

Voiculescu amenable Hopf von Neumann algebras with applications

2016 ◽  
Vol 15 (06) ◽  
pp. 1650079 ◽  
Author(s):  
Fatemeh Akhtari ◽  
Rasoul Nasr-Isfahani
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Continuous Functions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann

For a Hopf von Neumann algebra [Formula: see text], we give a fixed point characterization of Voiculescu amenability of [Formula: see text] in terms of modules over [Formula: see text]. As a consequence, we present some descriptions for amenability of locally compact groups in terms of certain associated Hopf von Neumann algebras. We finally apply this result to some modules of continuous functions on a multiplicative subsemigroup of [Formula: see text].

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