scholarly journals On the C ∗ -Algebra Generated by the Left Regular Representation of a Locally Compact Group

1994 ◽  
Vol 120 (2) ◽  
pp. 603 ◽  
Author(s):  
Erik Bedos
Keyword(s):  
Compact Group ◽  
Regular Representation ◽  
Locally Compact Group ◽  
Locally Compact ◽  
C Algebra ◽  
Left Regular Representation ◽  
Left Regular

scholarly journals On Group Von Neumann Algebras with Vector-Valued Functions

2018 ◽  
Vol 14 (1) ◽  
pp. 7596-7614
Author(s):  
Julien Esse Atto ◽  
Victor Kofi Assiamoua
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Regular Representation ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Von Neumann ◽  
Left Regular Representation ◽  
Left Regular ◽  
Vector Valued Functions ◽  
Vector Valued

Let G be a locally compact group equipped with a normalized Haar measure , A(G) the Fourier algebraof G and V N(G) the von Neumann algebra generated by the left regular representation of G. In this paper, we introduce the space V N(G;A) associated with the Fourier algebra A(G;A) for vector-valued functions on G, where A is a H-algebra. Some basic properties are discussed in the category of Banach space, and alsoin the category of operator space.

THE Ext-FUNCTOR OF COMPLETELY BOUNDED BI-COMODULES, INJECTIVITY AND COHOMOLOGY

2007 ◽  
Vol 18 (07) ◽  
pp. 761-781
Author(s):  
CHI-KEUNG NG
Keyword(s):  
Compact Group ◽  
Quantum Groups ◽  
Locally Compact Group ◽  
Locally Compact ◽  
C Algebra ◽  
Compact Quantum Groups

Suppose that S is a Hopf C*-algebra. Further to our study of the category of completely bounded S-comodules in [14], we will compare the Ext-functors for [Formula: see text] (the category of counital S-comodules) as well as for [Formula: see text] (the category of counital S-bicomodules) with the cohomology theories defined in [10]. The particular case of compact quantum groups as well as the cases of S=C0(G) and S = C*(G) (where G is a locally compact group) will be considered in more details. Moreover, we give some relations between the vanishing of the first dual cohomologies of C0(G) (respectively, C*(G)) and the injectivity of the bi-comodule U(G) (respectively, U(C*(G))).

scholarly journals THE GLIMM IDEAL SPACE OF A TWO-STEP NILPOTENT LOCALLY COMPACT GROUP

2001 ◽  
Vol 44 (3) ◽  
pp. 505-526 ◽  
Author(s):  
Eberhard Kaniuth ◽  
William Moran
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Locally Compact ◽  
C Algebra ◽  
Primary 22D25 ◽  
Secondary 22D10 ◽  
Necessary And Sufficient

AbstractFor a two-step nilpotent locally compact group $G$, we determine the Glimm ideal space of the group $C^*$-algebra $C^*(G)$ and its topology. This leads to necessary and sufficient conditions for $C^*(G)$ to be quasi-standard. Moreover, some results about the Glimm classes of points in the primitive ideal space $\mathrm{Prim}(C^*(G))$ are obtained.AMS 2000 Mathematics subject classification: Primary 22D25. Secondary 22D10

scholarly journals THE CROSSED PRODUCT BY A POINTWISE UNITARY ACTION ON A C*-ALGEBRA WITH CONTINUOUS TRACE

2001 ◽  
Vol 44 (1) ◽  
pp. 215-218
Author(s):  
Klaus Deicke
Keyword(s):  
Compact Group ◽  
Elementary Proof ◽  
Locally Compact Group ◽  
Crossed Product ◽  
Locally Compact ◽  
Primary 46L55 ◽  
C Algebra ◽  
Group A ◽  
Continuous Trace ◽  
Unitary Action

AbstractLet $G$ be a locally compact group, $A$ a continuous trace $C^*$-algebra, and $\alpha$ a pointwise unitary action of $G$ on $A$. It is a result of Olesen and Raeburn that if $A$ is separable and $G$ is second countable, then the crossed product $A\times_\alpha G$ has continuous trace. We present a new and much more elementary proof of this fact. Moreover, we do not even need the separability assumptions made on $A$ and $G$.AMS 2000 Mathematics subject classification: Primary 46L55

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