scholarly journals Fixed point property for Banach algebras associated to locally compact groups

2010 ◽  
Vol 258 (2) ◽  
pp. 357-372 ◽  
Author(s):  
Anthony To-Ming Lau ◽  
Peter F. Mah
Keyword(s):  
Fixed Point ◽  
Banach Algebras ◽  
Fixed Point Property ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Point Property ◽  
Locally Compact

scholarly journals A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Timothée Marquis
Keyword(s):  
Fixed Point ◽  
Finite Elements ◽  
Fixed Point Theorem ◽  
Lie Groups ◽  
Finite Rank ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Point Property ◽  
Locally Compact ◽  
Locally Finite

AbstractWe establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable stabilisers of points. As an application, we deduce amongst other things that all topological one-parameter subgroups of a real or complex Kac–Moody group are obtained by exponentiating ad-locally finite elements of the corresponding Lie algebra.

scholarly journals Fixed point characterization of left amenable Lau algebras

2004 ◽  
Vol 2004 (62) ◽  
pp. 3333-3338 ◽  
Author(s):  
R. Nasr-Isfahani
Keyword(s):  
Fixed Point ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Measure Algebra ◽  
Point Property ◽  
Locally Compact ◽  
Wide Range

The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras𝒜in terms of left Banach𝒜-modules. It also offers an application of this result to some Lau algebras related to a locally compact groupG, such as the Eymard-Fourier algebraA(G), the Fourier-Stieltjes algebraB(G), the group algebraL1(G), and the measure algebraM(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.

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.

scholarly journals THE MODULUS OF WEAKLY COMPACT MULTIPLIERS ON THE BANACH ALGEBRA L1(𝒢)** OF A LOCALLY COMPACT GROUP

2012 ◽  
Vol 86 (2) ◽  
pp. 315-321
Author(s):  
MOHAMMAD JAVAD MEHDIPOUR
Keyword(s):  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Weakly Compact ◽  
Necessary And Sufficient ◽  
Funct Anal

AbstractIn this paper we give a necessary and sufficient condition under which the answer to the open problem raised by Ghahramani and Lau (‘Multipliers and modulus on Banach algebras related to locally compact groups’, J. Funct. Anal. 150 (1997), 478–497) is positive.

scholarly journals ON n-IDEAL AMENABILITY OF CERTAIN BANACH ALGEBRAS

2011 ◽  
Vol 86 (1) ◽  
pp. 90-99 ◽  
Author(s):  
ZEINAB KAMALI ◽  
MEHDI NEMATI
Keyword(s):  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Ideal Amenability ◽  
Segal Algebras

AbstractIn this paper we consider some notions of amenability such as ideal amenability, n-ideal amenability and approximate n-ideal amenability. The first two were introduced and studied by Gordji, Yazdanpanah and Memarbashi. We investigate some properties of certain Banach algebras in each of these classes. Results are also given for Segal algebras on locally compact groups.

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