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.

scholarly journals META-CENTRALIZERS OF NON-LOCALLY COMPACT GROUP ALGEBRAS

2014 ◽  
Vol 57 (2) ◽  
pp. 349-364 ◽  
Author(s):  
S. V. LUDKOVSKY
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact

AbstractMeta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with meta-centralizers.

scholarly journals Multinorms and Approximate Amenability of Weighted Group Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Saman Ghaderkhani
Keyword(s):  
Weight Function ◽  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Approximate Amenability

Let G be a locally compact group, and take p,q with 1≤p,q<∞. We prove that, for any left (p,q)-multiinvariant functional on L∞(G) and for any weight function ω≥1 on G, the approximate amenability of the Banach algebra L1(G,ω) implies the left (p,q)-amenability of G, but in general the opposite is not true. Our proof uses the notion of multinorms. We also investigate the approximate amenability of M(G,ω).

scholarly journals INVOLUTIONS ON THE SECOND DUALS OF GROUP ALGEBRAS AND A MULTIPLIER PROBLEM

2007 ◽  
Vol 50 (1) ◽  
pp. 153-161 ◽  
Author(s):  
H. Farhadi ◽  
F. Ghahramani
Keyword(s):  
Sufficient Conditions ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Dual Algebra ◽  
Amenable Subgroup ◽  
Second Dual ◽  
Necessary And Sufficient ◽  
Bounded Continuous Functions

AbstractWe show that if a locally compact group $G$ is non-discrete or has an infinite amenable subgroup, then the second dual algebra $L^1(G)^{**}$ does not admit an involution extending the natural involution of $L^1(G)$. Thus, for the above classes of groups we answer in the negative a question raised by Duncan and Hosseiniun in 1979. We also find necessary and sufficient conditions for the dual of certain left-introverted subspaces of the space $C_b(G)$ (of bounded continuous functions on $G$) to admit involutions. We show that the involution problem is related to a multiplier problem. Finally, we show that certain non-trivial quotients of $L^1(G)^{**}$ admit involutions.

scholarly journals The continuity of derivations from group algebras: factorizable and connected groups

1992 ◽  
Vol 52 (2) ◽  
pp. 185-204 ◽  
Author(s):  
George Willis
Keyword(s):  
Finite Number ◽  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Abelian Subgroups

AbstractA group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.

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.

Weak*- continuous homomorphisms of Fourier–Stieltjes algebras

2008 ◽  
Vol 145 (1) ◽  
pp. 107-120 ◽  
Author(s):  
MONICA ILIE ◽  
ROSS STOKKE
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Algebra Homomorphism ◽  
Affine Mapping ◽  
Locally Compact ◽  
Amenable Groups ◽  
Affine Map ◽  
Piecewise Affine ◽  
Open Map

AbstractFor a locally compact group G, let B(G) denote its Fourier–Stieltjes algebra. Any continuous, piecewise affine map α: Y ⊂ H → G induces a completely bounded algebra homomorphism jα: B(G) → B(H) [14, 15] and we prove that jα is w* – w* continuous if and only if α is an open map. This extends one of the main results in [3], due to M.B. Bekka, E. Kaniuth, A.T. Lau and G. Schlichting. Several classical theorems regarding isomorphisms and extensions of homomorphisms on group algebras of abelian groups are extended to the setting of Fourier–Stieltjes algebras of amenable groups. As applications, when G is amenable we provide complete characterizations of those maps between Fourier–Stieltjes algebras that are either associated to a piecewise affine mapping, or are completely bounded and w* – w* continuous.

Minimal ideals in group algebras and their biduals

1996 ◽  
Vol 120 (3) ◽  
pp. 475-488 ◽  
Author(s):  
J. W. Baker ◽  
M. Filali
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Finite Dimensional

AbstractLet G be a locally compact group and F a left introverted subalgebra of C(G). For each of the algebras L1(G), M(G), F* and L∞(G)* we determine the finite-dimensional minimal left ideals of the algebra (if any); in some cases we also determine the finite-dimensional minimal two-sided ideals, and in certain cases show that all minimal ideals of the algebra are finite-dimensional.

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