scholarly journals ON THE TOPOLOGICAL CENTRE OF L1(G/H)**

2012 ◽  
Vol 86 (1) ◽  
pp. 119-125 ◽  
Author(s):  
R. RAISI TOUSI ◽  
R. A. KAMYABI-GOL ◽  
H. R. EBRAHIMI VISHKI
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Compact Subgroup ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
General Criterion ◽  
Unified Approach ◽  
Locally Compact ◽  
Topological Centre

AbstractLet G be a locally compact group and H be a compact subgroup of G. Using a general criterion established by Neufang [‘A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis’, Arch. Math.82(2) (2004), 164–171], we show that the Banach algebra L1(G/H) is strongly Arens irregular for a large class of locally compact groups.

scholarly journals Completely continuous elements of Banach algebras related to locally compact groups

2007 ◽  
Vol 76 (1) ◽  
pp. 49-54 ◽  
Author(s):  
M. J. Mehdipour ◽  
R. Nasr-Isfahani
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Completely Continuous ◽  
Measurable Functions

Let G be a locally compact group and be the Banach space of all essentially bounded measurable functions on G vansihing an infinity. Here, we study some families of right completely continuous elements in the Banach algebra equipped with an Arens type product. As the main result, we show that has a certain right completely continuous element if and only if G is compact.

Lp-spaces on locally compact groups

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
H. Samea
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Lp Spaces

AbstractIn this paper, some relations between L p-spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras L p(G) ∩ L 1(G) (1 < p ≤ ∞), and A p(G) ∩ L 1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable.

scholarly journals COMPACT LEFT MULTIPLIERS ON BANACH ALGEBRAS RELATED TO LOCALLY COMPACT GROUPS

2009 ◽  
Vol 79 (2) ◽  
pp. 227-238 ◽  
Author(s):  
M. J. MEHDIPOUR ◽  
R. NASR-ISFAHANI
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Completely Continuous ◽  
Left Multiplier

AbstractWe deal with the dual Banach algebras $L_0^\infty (G)^*$ for a locally compact group G. We investigate compact left multipliers on $L_0^\infty (G)^*$, and prove that the existence of a compact left multiplier on $L_0^\infty (G)^*$ is equivalent to compactness of G. We also describe some classes of left completely continuous elements in $L_0^\infty (G)^*$.

scholarly journals THE MODULUS OF WEAKLY COMPACT MULTIPLIERS ON THE BANACH ALGEBRA L1(𝒢)** OF A LOCALLY COMPACT GROUP

2012 ◽  
Vol 86 (2) ◽  
pp. 315-321
Author(s):  
MOHAMMAD JAVAD MEHDIPOUR
Keyword(s):  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Weakly Compact ◽  
Necessary And Sufficient ◽  
Funct Anal

AbstractIn this paper we give a necessary and sufficient condition under which the answer to the open problem raised by Ghahramani and Lau (‘Multipliers and modulus on Banach algebras related to locally compact groups’, J. Funct. Anal. 150 (1997), 478–497) is positive.

scholarly journals Ends of locally compact groups and their coset spaces

1974 ◽  
Vol 17 (3) ◽  
pp. 274-284 ◽  
Author(s):  
C. H. Houghton
Keyword(s):  
Compact Group ◽  
Direct Product ◽  
Compact Space ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Countable Base ◽  
Locally Compact ◽  
Coset Spaces ◽  
Compact Boundary

Freudenthal [5, 7] defined a compactification of a rim-compact space, that is, a space having a base of open sets with compact boundary. The additional points are called ends and Freudenthal showed that a connected locally compact non-compact group having a countable base has one or two ends. Later, Freudenthal [8], Zippin [16], and Iwasawa [11] showed that a connected locally compact group has two ends if and only if it is the direct product of a compact group and the reals.

scholarly journals A note on the duality of locally compact groups

1968 ◽  
Vol 9 (2) ◽  
pp. 87-91 ◽  
Author(s):  
J. W. Baker
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Group Topology ◽  
Locally Compact ◽  
Natural Way

Let H be a group of characters on an (algebraic) abelian group G. In a natural way, we may regard G as a group of characters on H. In this way, we obtain a duality between the two groups G and H. One may pose several problems about this duality. Firstly, one may ask whether there exists a group topology on G for which H is precisely the set of continuous characters. This question has been answered in the affirmative in [1]. We shall say that such a topology is compatible with the duality between G and H. Next, one may ask whether there exists a locally compact group topology on G which is compatible with a given duality and, if so, whether there is more than one such topology. It is this second question (previously considered by other authors, to whom we shall refer below) which we shall consider here.

A decomposition theorem for locally compact groups

2019 ◽  
Vol 26 (1) ◽  
pp. 29-33
Author(s):  
Sanjib Basu ◽  
Krishnendu Dutta
Keyword(s):  
Compact Group ◽  
Lebesgue Point ◽  
Decomposition Theorem ◽  
Locally Compact Group ◽  
The Other ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Interesting Connection

Abstract We prove that, under certain restrictions, every locally compact group equipped with a nonzero, σ-finite, regular left Haar measure can be decomposed into two small sets, one of which is small in the sense of measure and the other is small in the sense of category, and all such decompositions originate from a generalised notion of a Lebesgue point. Incidentally, such class of topological groups for which this happens turns out to be metrisable. We also observe an interesting connection between Luzin sets in such spaces and decompositions of the above type.

scholarly journals POROSITY OF CERTAIN SUBSETS OF LEBESGUE SPACES ON LOCALLY COMPACT GROUPS

2012 ◽  
Vol 88 (1) ◽  
pp. 113-122 ◽  
Author(s):  
I. AKBARBAGLU ◽  
S. MAGHSOUDI
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Young’S Inequality ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
First Category ◽  
Young's Inequality ◽  
Set Of First Category

AbstractLet $G$ be a locally compact group. In this paper, we show that if $G$ is a nondiscrete locally compact group, $p\in (0, 1)$ and $q\in (0, + \infty ] $, then $\{ (f, g)\in {L}^{p} (G)\times {L}^{q} (G): f\ast g\text{ is finite } \lambda \text{-a.e.} \} $ is a set of first category in ${L}^{p} (G)\times {L}^{q} (G)$. We also show that if $G$ is a nondiscrete locally compact group and $p, q, r\in [1, + \infty ] $ such that $1/ p+ 1/ q\gt 1+ 1/ r$, then $\{ (f, g)\in {L}^{p} (G)\times {L}^{q} (G): f\ast g\in {L}^{r} (G)\} $, is a set of first category in ${L}^{p} (G)\times {L}^{q} (G)$. Consequently, for $p, q\in [1+ \infty )$ and $r\in [1, + \infty ] $ with $1/ p+ 1/ q\gt 1+ 1/ r$, $G$ is discrete if and only if ${L}^{p} (G)\ast {L}^{q} (G)\subseteq {L}^{r} (G)$; this answers a question raised by Saeki [‘The ${L}^{p} $-conjecture and Young’s inequality’, Illinois J. Math. 34 (1990), 615–627].

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 On the real rank of $C^\ast$-algebras of nilpotent locally compact groups

2012 ◽  
Vol 110 (1) ◽  
pp. 99 ◽  
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Compact Group ◽  
Heisenberg Group ◽  
Identity Element ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Real Rank ◽  
Connected Component ◽  
Locally Compact ◽  
The Real

If $G$ is an almost connected, nilpotent, locally compact group then the real rank of the $C^\ast$-algebra $C^\ast (G)$ is given by $\operatorname {RR} (C^\ast (G)) = \operatorname {rank} (G/[G,G]) = \operatorname {rank} (G_0/[G_0,G_0])$, where $G_0$ is the connected component of the identity element. In particular, for the continuous Heisenberg group $G_3$, $\operatorname {RR} C^\ast (G_3))=2$.

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