Concerning the Second Dual of the Group Algebra of a Locally Compact Group

1990 ◽  
Vol s2-41 (3) ◽  
pp. 445-460 ◽  
Author(s):  
Anthony To-Ming Lau ◽  
John Pym
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Second Dual

scholarly journals ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER CONVOLUTION ALGEBRAS

2011 ◽  
Vol 84 (2) ◽  
pp. 177-185
Author(s):  
RASOUL NASR-ISFAHANI ◽  
SIMA SOLTANI RENANI
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Dual Space ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Measure Algebra ◽  
Locally Compact ◽  
Convolution Algebras ◽  
Uniformly Continuous

AbstractFor a locally compact group G, let LUC(G) denote the space of all left uniformly continuous functions on G. Here, we investigate projectivity, injectivity and flatness of LUC(G) and its dual space LUC(G)* as Banach left modules over the group algebra as well as the measure algebra of G.

scholarly journals Non commutative convolution measure algebras with no proper L-ideals

1989 ◽  
Vol 40 (1) ◽  
pp. 13-23 ◽  
Author(s):  
Sahl Fadul Albar
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Dimensional Representation ◽  
Locally Compact ◽  
Finite Dimensional Representation ◽  
Finite Dimensional

We study non-commutative convolution measure algebras satisfying the condition in the title and having an involution with a non-degenerate finite dimensional *-representation. We show first that the group algebra L1(G) of a locally compact group G satisfies these conditions. Then we show that to a given algebra A with the above conditions there corresponds a locally compact group G such that A is a * and L-subalgebra of M(G) and such that the enveloping C*-algebra of A is *isomorphic to C*(G). Finally we show for certain groups that L1(G) is the only example of such algebras, thus giving a characterisation of L1(G).

On invariant convex subsets in algebras defined on a locally compact group G

2012 ◽  
Vol 49 (3) ◽  
pp. 301-314
Author(s):  
Ali Ghaffari
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Left Translation ◽  
Measure Algebra ◽  
Locally Compact ◽  
Translation Invariant ◽  
Second Dual ◽  
Necessary And Sufficient ◽  
Convex Subsets

Suppose that A is either the Banach algebra L1(G) of a locally compact group G, or measure algebra M(G), or other algebras (usually larger than L1(G) and M(G)) such as the second dual, L1(G)**, of L1(G) with an Arens product, or LUC(G)* with an Arenstype product. The left translation invariant closed convex subsets of A are studied. Finally, we obtain necessary and sufficient conditions for LUC(G)* to have 1-dimensional left ideals.

Isomorphisms between the second duals of group algebras of locally compact groups

1996 ◽  
Vol 119 (4) ◽  
pp. 657-663 ◽  
Author(s):  
Hamid-Reza Farhadi
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Algebra Isomorphism ◽  
Continuous Automorphism

AbstractLet G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).

Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras

2017 ◽  
Vol 69 (1) ◽  
pp. 3-20 ◽  
Author(s):  
F. Ghahramani ◽  
S. Zadeh
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Order Structure ◽  
Algebra Structure ◽  
Locally Compact ◽  
Second Dual ◽  
Beurling Algebras ◽  
Continuous Weight

AbstractLet G be a locally compact group and let ω be a continuous weight on G. We show that for each of the Banach algebras L1(G,ω ), M(G,ω ), LUC(G,ω -1)*, and L1(G, ω)**, the order structure combined with the algebra structure determines the weighted group.

scholarly journals The modulus of operators on group algebras

2004 ◽  
Vol 35 (2) ◽  
pp. 95-100
Author(s):  
Ali. Ghaffari
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Second Dual

Let $ G $ be a locally compact group. In this paper, we study the modulus of right multipliers on second dual of group algebras and modulus of operators on $ L^\infty (G)$ which commute with convolutions.

Module Homomorphisms of the Dual Modules of Convolution Banach Algebras

1992 ◽  
Vol 35 (2) ◽  
pp. 180-185 ◽  
Author(s):  
F. Ghahramani ◽  
J. P. Mcclure
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Banach Module ◽  
Locally Compact ◽  
Arens Product ◽  
Convolution Algebra

AbstractSuppose that A is either the group algebra L1 (G) of a locally compact group G, or the Volterra algebra or a weighted convolution algebra with a regulated weight. We characterize: a) Module homomorphisms of A*, when A* is regarded an A** left Banach module with the Arens product, b) all the weak*-weak* continuous left multipliers of A**.

Kernels and cokernels in the category of augmented involutive stereotype algebras

2019 ◽  
Vol 19 (06) ◽  
pp. 2050108
Author(s):  
S. S. Akbarov
Keyword(s):  
Hopf Algebra ◽  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Pontryagin Duality ◽  
Locally Compact

We prove several properties of kernels and cokernels in the category of augmented involutive stereotype algebras: (1) this category has kernels and cokernels, (2) the cokernel is preserved under the passage to the group stereotype algebras, and (3) the notion of cokernel allows to prove that the continuous envelope [Formula: see text] of the group algebra of a compact buildup of an abelian locally compact group is an involutive Hopf algebra in the category of stereotype spaces [Formula: see text]. The last result plays an important role in the generalization of the Pontryagin duality for arbitrary Moore groups.

scholarly journals Biflatness and Pseudo-Amenability of Segal Algebras

2010 ◽  
Vol 62 (4) ◽  
pp. 845-869 ◽  
Author(s):  
Ebrahim Samei ◽  
Nico Spronk ◽  
Ross Stokke
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Segal Algebras

AbstractWe investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group G.

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