scholarly journals Cyclicity of the left regular representation of a locally compact group

2018 ◽  
Vol 48 (3) ◽  
pp. 1015-1018
Author(s):  
Zsolt Tanko
Keyword(s):  
Compact Group ◽  
Regular Representation ◽  
Locally Compact Group ◽  
Locally Compact ◽  
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.

Some Results on the Center of an Algebra of Operators on VN(G) for the Heisenberg group

1981 ◽  
Vol 33 (6) ◽  
pp. 1469-1486 ◽  
Author(s):  
C. Cecchini ◽  
A. Zappa
Keyword(s):  
Compact Group ◽  
Heisenberg Group ◽  
Von Neumann Algebra ◽  
Regular Representation ◽  
Locally Compact Group ◽  
Linear Operators ◽  
Locally Compact ◽  
Bounded Linear ◽  
Von Neumann ◽  
Algebra Of Operators

Let G be an amenable locally compact group. We will use the terminology of [3] and denote by VN(G) the Von Neumann algebra of the regular representation and by A(G) its predual, which is the algebra of the coefficients of the regular representation. The Von Neumann algebra VN(G) is, in a natural fashion, a module with respect to A(G) [3].The algebra of bounded linear operators on VN(G), which commute with the action of A(G), has been studied in [6] and in [1]. If UCB(Ĝ) is the space of the elements of VN(G) of the form vT, for some v in A(G) and some T in VN(G) (see for instance [4]), in [6] and in [1] it is proved that, for any amenable locally compact group there exists an isometric bijection between and UCB(Ĝ)*.

scholarly journals A COMPACT QUALITATIVE UNCERTAINTY PRINCIPLE FOR SOME NONUNIMODULAR GROUPS

2018 ◽  
Vol 99 (1) ◽  
pp. 114-120
Author(s):  
WASSIM NASSERDDINE
Keyword(s):  
Regular Representation ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compactly Supported ◽  
Finite Dimensional ◽  
Left Regular Representation ◽  
Left Regular ◽  
Compact Abelian Groups ◽  
Qualitative Uncertainty ◽  
The Fourier Transform

Let $G$ be a separable locally compact group with type $I$ left regular representation, $\widehat{G}$ its dual, $A(G)$ its Fourier algebra and $f\in A(G)$ with compact support. If $G=\mathbb{R}$ and the Fourier transform of $f$ is compactly supported, then, by a classical Paley–Wiener theorem, $f=0$. There are extensions of this theorem for abelian and some unimodular groups. In this paper, we prove that if $G$ has no (nonempty) open compact subsets, $\hat{f}$, the regularised Fourier cotransform of $f$, is compactly supported and $\text{Im}\,\hat{f}$ is finite dimensional, then $f=0$. In connection with this result, we characterise locally compact abelian groups whose identity components are noncompact.

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