scholarly journals Geometric Properties of Coefficient Function Spaces Determined by Unitary Representations of a Locally Compact Group

1995 ◽  
Vol 193 (2) ◽  
pp. 390-405 ◽  
Author(s):  
A. Belanger ◽  
B.E. Forrest
Keyword(s):  
Compact Group ◽  
Function Spaces ◽  
Locally Compact Group ◽  
Unitary Representations ◽  
Coefficient Function ◽  
Locally Compact ◽  
Geometric Properties

scholarly journals On isomorphisms between weighted -algebras

2020 ◽  
pp. 1-14
Author(s):  
Yulia Kuznetsova ◽  
Safoura Zadeh
Keyword(s):  
Compact Group ◽  
Composition Operators ◽  
Function Spaces ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Classical Function ◽  
Continuous Weight

Abstract Let G be a locally compact group and let $\omega $ be a continuous weight on G. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$ -algebras. As a result, we extend previous results of Edwards, Parrott, and Strichartz on algebra isomorphisms between $L^p$ -algebras to the setting of weighted $L^p$ -algebras. We then study the automorphisms of certain weighted $L^p$ -algebras on integers, applying known results on composition operators to classical function spaces.

Compactness of a Locally Compact Group G and Geometric Properties of Ap(G)

1996 ◽  
Vol 48 (6) ◽  
pp. 1273-1285 ◽  
Author(s):  
Tianxuan Miao
Keyword(s):  
Topological Group ◽  
Compact Group ◽  
Multiplication Operator ◽  
Locally Compact Group ◽  
Compact Groups ◽  
Locally Compact ◽  
Geometric Properties ◽  
Nikodym Property ◽  
Group A ◽  
Locally Compact Topological Group

AbstractLet G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property, Dunford-Pettis property and Schur property of Ap(G), and the properties of the multiplication operator on PFp(G). We extend and improve several results of Lau and Ülger [17] to Ap(G) and Bp(G) for arbitrary p.

scholarly journals The von Neumann kernel of a locally compact group

1984 ◽  
Vol 36 (2) ◽  
pp. 279-286 ◽  
Author(s):  
Sheldon Rothman ◽  
Helen Strassberg
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Unitary Representations ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Neumann Kernel

AbstractFor a locally compact group G, the von Neumann kernel, n(G), is the intersection of the kernels of the finite dimensional (continuous) unitary representations of G. In this paper we calculate n(G) explicitly for a general connected locally compact group and for certain classes of non-connected groups.

Convolution on L p-spaces of a locally compact group

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Fatemeh Abtahi ◽  
Rasoul Nasr-Isfahani ◽  
Ali Rejali
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Function Spaces ◽  
Locally Compact Group ◽  
Necessary And Sufficient Conditions ◽  
Locally Compact ◽  
Necessary And Sufficient

AbstractWe have recently shown that, for 2 < p < ∞, a locally compact group G is compact if and only if the convolution multiplication f * g exists for all f, g ∈ L p(G). Here, we study the existence of f * g for all f, g ∈ L p(G) in the case where 0 < p ≤ 2. Also, for 0 < p < ∞, we offer some necessary and sufficient conditions for L p(G) * L p(G) to be contained in certain function spaces on G.

scholarly journals Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

2006 ◽  
Vol 98 (2) ◽  
pp. 182 ◽  
Author(s):  
Ross Stokke
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Unitary Representations ◽  
Locally Compact ◽  
Von Neumann ◽  
C Algebras

Amenable unitary representations of a locally compact group, $G$, are studied in terms of associated coefficient subspaces of the Fourier-Stieltjes algebra $B(G)$, and in terms of the existence of invariant and multiplicative states on associated von Neumann and $C^*$-algebras. We introduce Fourier algebras and reduced Fourier-Stieltjes algebras associated to arbitrary representations, and study amenable representations in relation to these algebras.

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