1. CJM 2016 (vol 69 pp. 3)
 Ghahramani, F.; Zadeh, S.

Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras
Let $G$ be a locally compact group and let $\omega$ be a continuous
weight on $G$. We show that for each of the Banach algebras $L^1(G,\omega)$,
$M(G,\omega)$, $LUC(G,\omega^{1})^*$ and $L^1(G,\omega)^{**}$,
the order structure combined with the algebra structure determines
the weighted group.
Keywords:locally compact group, Beurling algebra, Arens product, topological group isomorphism, bipositive algebra isomorphism Categories:43A20, 43A22 

2. CJM 2016 (vol 69 pp. 434)
 Lee, Hun Hee; Youn, Sanggyun

New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups
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
of 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 finitely
generated discrete groups with connection to the growth rate
of the group.
Keywords:Fourier algebra, convolution algebra, operator algebra, Beurling algebra Categories:43A20, 43A30, 47L30, 47L25 

3. CJM 2010 (vol 62 pp. 845)
 Samei, Ebrahim; Spronk, Nico; Stokke, Ross

Biflatness and PseudoAmenability of Segal Algebras
We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, $L^1(G)$, and the Fourier algebra, $A(G)$, of a locally compact group~$G$.
Keywords:Segal algebra, pseudoamenable Banach algebra, biflat Banach algebra Categories:43A20, 43A30, 46H25, 46H10, 46H20, 46L07 

4. CJM 2006 (vol 58 pp. 768)
 Hu, Zhiguo; Neufang, Matthias

Decomposability of von Neumann Algebras and the Mazur Property of Higher Level
The decomposability
number of a von Neumann algebra $\m$ (denoted by $\dec(\m)$) is the
greatest cardinality of a family of pairwise orthogonal nonzero
projections in $\m$. In this paper, we explore the close
connection between $\dec(\m)$ and the cardinal level of the Mazur
property for the predual $\m_*$ of $\m$, the study of which was
initiated by the second author. Here, our main focus is on
those von Neumann algebras whose preduals constitute such
important Banach algebras on a locally compact group $G$ as the
group algebra $\lone$, the Fourier algebra $A(G)$, the measure
algebra $M(G)$, the algebra $\luc^*$, etc. We show that for
any of these von Neumann algebras, say $\m$, the cardinal number
$\dec(\m)$ and a certain cardinal level of the Mazur property of $\m_*$
are completely encoded in the underlying group structure. In fact,
they can be expressed precisely by two dual cardinal
invariants of $G$: the compact covering number $\kg$ of $G$ and
the least cardinality $\bg$ of an open basis at the identity of
$G$. We also present an application of the Mazur property of higher
level to the topological centre problem for the Banach algebra
$\ag^{**}$.
Keywords:Mazur property, predual of a von Neumann algebra, locally compact group and its cardinal invariants, group algebra, Fourier algebra, topological centre Categories:22D05, 43A20, 43A30, 03E55, 46L10 

5. CJM 2001 (vol 53 pp. 944)
 Ludwig, J.; MolitorBraun, C.

ReprÃ©sentations irrÃ©ductibles bornÃ©es des groupes de Lie exponentiels
Let $G$ be a solvable exponential Lie group. We characterize all the
continuous topologically irreducible bounded representations $(T,
\calU)$ of $G$ on a Banach space $\calU$ by giving a $G$orbit in
$\frn^*$ ($\frn$ being the nilradical of $\frg$), a topologically
irreducible representation of $L^1(\RR^n, \o)$, for a certain weight
$\o$ and a certain $n \in \NN$, and a topologically simple extension
norm. If $G$ is not symmetric, \ie, if the weight $\o$ is
exponential, we get a new type of representations which are
fundamentally different from the induced representations.
Soit $G$ un groupe de Lie r\'esoluble exponentiel. Nous
caract\'erisons toutes les repr\'esentations $(T, \calU)$ continues
born\'ees topologiquement irr\'eductibles de $G$ dans un espace de
Banach $\calU$ \`a l'aide d'une $G$orbite dans $\frn^*$ ($\frn$
\'etant le radical nilpotent de $\frg$), d'une repr\'esentation
topologiquement irr\'eductible de $L^1(\RR^n, \o)$, pour un certain
poids $\o$ et un certain $n \in \NN$, d'une norme d'extension
topologiquement simple. Si $G$ n'est pas sym\'etrique, c. \`a d. si
le poids $\o$ est exponentiel, nous obtenons un nouveau type de
repr\'esentations qui sont fondamentalement diff\'erentes des
repr\'esentations induites.
Keywords:groupe de Lie rÃ©soluble exponentiel, reprÃ©sentation bornÃ©e topologiquement irrÃ©ductible, orbite, norme d'extension, sousespace invariant, idÃ©al premier, idÃ©al primitif Category:43A20 

6. CJM 1999 (vol 51 pp. 96)
 Rösler, Margit; Voit, Michael

Partial Characters and Signed Quotient Hypergroups
If $G$ is a closed subgroup of a commutative hypergroup $K$, then the
coset space $K/G$ carries a quotient hypergroup structure. In this
paper, we study related convolution structures on $K/G$ coming from
deformations of the quotient hypergroup structure by certain functions
on $K$ which we call partial characters with respect to $G$. They are
usually not probabilitypreserving, but lead to socalled signed
hypergroups on $K/G$. A first example is provided by the Laguerre
convolution on $\left[ 0,\infty \right[$, which is interpreted as a
signed quotient hypergroup convolution derived from the Heisenberg
group. Moreover, signed hypergroups associated with the Gelfand pair
$\bigl( U(n,1), U(n) \bigr)$ are discussed.
Keywords:quotient hypergroups, signed hypergroups, Laguerre convolution, Jacobi functions Categories:43A62, 33C25, 43A20, 43A90 
