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.

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 Some properties of locally compact groups

1967 ◽  
Vol 7 (4) ◽  
pp. 433-454 ◽  
Author(s):  
Neil W. Rickert
Keyword(s):  
Compact Group ◽  
Lie Groups ◽  
Locally Compact Group ◽  
Factor Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Arcwise Connected ◽  
New Formulation

In this paper a number of questions about locally compact groups are studied. The structure of finite dimensional connected locally compact groups is investigated, and a fairly simple representation of such groups is obtained. Using this it is proved that finite dimensional arcwise connected locally compact groups are Lie groups, and that in general arcwise connected locally compact groups are locally connected. Semi-simple locally compact groups are then investigated, and it is shown that under suitable restrictions these satisfy many of the properties of semi-simple Lie groups. For example, a factor group of a semi-simple locally compact group is semi-simple. A result of Zassenhaus, Auslander and Wang is reformulated, and in this new formulation it is shown to be true under more general conditions. This fact is used in the study of (C)-groups in the sense of K. Iwasawa.

scholarly journals Operator Amenability of the Fourier Algebra in the cb-Multiplier Norm

2007 ◽  
Vol 59 (5) ◽  
pp. 966-980 ◽  
Author(s):  
Brian E. Forrest ◽  
Volker Runde ◽  
Nico Spronk
Keyword(s):  
Compact Group ◽  
Free Group ◽  
Discrete Group ◽  
Amenable Group ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Residually Finite ◽  
Finite Dimensional

AbstractLet G be a locally compact group, and let Acb(G) denote the closure of A(G), the Fourier algebra of G, in the space of completely boundedmultipliers of A(G). If G is a weakly amenable, discrete group such that C*(G) is residually finite-dimensional, we show that Acb(G) is operator amenable. In particular, Acb() is operator amenable even though , the free group in two generators, is not an amenable group. Moreover, we show that if G is a discrete group such that Acb(G) is operator amenable, a closed ideal of A(G) is weakly completely complemented in A(G) if and only if it has an approximate identity bounded in the cb-multiplier norm.

scholarly journals On One-parameter Subgroups in Finite Dimensional Locally Compact Group with No Small Subgroups

1952 ◽  
Vol 4 ◽  
pp. 89-96
Author(s):  
Masatake Kuranishi
Keyword(s):  
Topological Group ◽  
Compact Group ◽  
Lie Group ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Finite Dimensional ◽  
Locally Compact Topological Group

Let G be a locally compact topological group and let U be a neighborhood of the identity in G. A curve g(λ) (|λ| ≦ 1) in G, which satisfies the conditions, g(s)g(t) = g(s + t) (|s|, |f|, |s + t| ≦ l),is called a one-parameter subgroup of G. If there exists a neighborhood U1 of the identity in G such that for every element x of U1 there exists a unique one-parameter subgroup g(λ) which is contained in U and g(1) =x, we shall call, for the sake of simplicity, that U has the property (S). It is well known that the neighborhoods of the identity in a Lie group have the property (S). More generally it is proved that if G is finite dimensional, locally connected, and is without small subgroups, G has the same property. In this note, these theorems will be generalized to the case when G is unite dimensional and without small subgroups.

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 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).

MARTINGALE CHARACTERIZATIONS OF INCREMENT PROCESSES IN A LOCALLY COMPACT GROUP

2003 ◽  
Vol 06 (04) ◽  
pp. 563-595 ◽  
Author(s):  
HERBERT HEYER ◽  
GYULA PAP
Keyword(s):  
Compact Group ◽  
Martingale Problem ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Finite Dimensional Representation ◽  
Finite Dimensional ◽  
Fourier Theory ◽  
Group A ◽  
Tensor Square ◽  
Special Case

Martingale characterizations and the related martingale problem are studied for processes with independent (not necessarily stationary) increments in an arbitrary locally compact group. In the special case of a compact Lie group, a Lévy-type characterization is given in terms of a faithful finite dimensional representation of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups associated with the increment processes.

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.

scholarly journals The von Neumann kernel of a locally compact group

1984 ◽  
Vol 36 (2) ◽  
pp. 279-286 ◽  
Author(s):  
Sheldon Rothman ◽  
Helen Strassberg
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Unitary Representations ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Neumann Kernel

AbstractFor a locally compact group G, the von Neumann kernel, n(G), is the intersection of the kernels of the finite dimensional (continuous) unitary representations of G. In this paper we calculate n(G) explicitly for a general connected locally compact group and for certain classes of non-connected groups.

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