Amenability of Weighted Convolution Algebras on Locally Compact Groups

1990 ◽  
Vol 319 (2) ◽  
pp. 765 ◽  
Author(s):  
Niels Gronbaek
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Convolution Algebras

scholarly journals New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups

2017 ◽  
Vol 69 (02) ◽  
pp. 434-452 ◽  
Author(s):  
Hun Hee Lee ◽  
Sang-gyun Youn
Keyword(s):  
Growth Rate ◽  
Lie Groups ◽  
Operator Algebra ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Discrete Groups ◽  
Locally Compact ◽  
Real Dimension ◽  
Convolution Algebras ◽  
Deformed Algebras

Abstract In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information about the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we investigate complete representability as an operator algebra of deformed Fourier algebras on some ûnitely generated discrete groups with connection to the growth rate of the group.

On the Lp-conjecture for locally compact groups

2007 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
F. Abtahi ◽  
R. Nasr-Isfahani ◽  
A. Rejali
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

Ergodic actions of group extensions on von Neumann algebras

1989 ◽  
Vol 112 (1-2) ◽  
pp. 71-112
Author(s):  
Klaus Thomsen
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Fixed Point Algebra ◽  
Atomic Centre

SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.

Locally compact groups with permutable closed subgroups

2021 ◽  
Vol 390 ◽  
pp. 107894
Author(s):  
Wolfgang Herfort ◽  
Karl H. Hofmann ◽  
Francesco G. Russo
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact
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