Hecke **-algebras on locally compact hypergroups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
Bentolhoda Sadathoseyni
Keyword(s):  
Compact Group ◽  
Hecke Algebras ◽  
Locally Compact Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Basic Properties ◽  
Necessary And Sufficient

AbstractIn this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke {*}-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative {*}-algebra if and only if K is a locally compact group.

scholarly journals Some properties of distal actions on locally compact groups

2017 ◽  
Vol 39 (5) ◽  
pp. 1340-1360 ◽  
Author(s):  
C. R. E. RAJA ◽  
RIDDHI SHAH
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Contraction Group

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We obtain a decomposition for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.

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 Chaos for Cosine Operator Functions on Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Locally Compact Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Direct Sum ◽  
Cosine Operator ◽  
Weight Condition ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Necessary And Sufficient

Let1≤p<∞andGbe a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue spaceLp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.

scholarly journals A Riemann integral in a locally compact Hausdorff space

1986 ◽  
Vol 41 (1) ◽  
pp. 115-137 ◽  
Author(s):  
S. I. Ahmed ◽  
W. F. Pfeffer
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Sufficient Condition ◽  
Lebesgue Integral ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Riemann Integral ◽  
Variational Integrals ◽  
Necessary And Sufficient ◽  
Locally Compact Hausdorff Space

AbstractWe present a systematic and self-contained exposition of the generalized Riemann integral in a locally compact Hausdorff space, and we show that it is equivalent to the Perron and variational integrals. We also give a necessary and sufficient condition for its equivalence to the Lebesgue integral with respect to a suitably chosen measure.

Comaximal factorization of lifting ideals

2020 ◽  
pp. 2250044
Author(s):  
Esmaeil Rostami ◽  
Sina Hedayat ◽  
Reza Nekooei ◽  
Somayeh Karimzadeh
Keyword(s):  
Commutative Ring ◽  
Proper Ideal ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Approach ◽  
Ideal Formula ◽  
Basic Properties ◽  
Necessary And Sufficient

A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.

scholarly journals A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS
Keyword(s):  
Limit Theorem ◽  
Dynamical Systems ◽  
Compact Group ◽  
Short Proof ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Occupation Measure ◽  
Necessary And Sufficient Condition ◽  
Occupation Measures ◽  
Necessary And Sufficient

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.

Properties of bisect-diagonal quadrilaterals

2017 ◽  
Vol 101 (551) ◽  
pp. 214-226 ◽  
Author(s):  
Martin Josefsson
Keyword(s):  
General Class ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
Necessary And Sufficient

The general class of quadrilaterals where one diagonal is bisected by the other diagonal has appeared very rarely in the geometrical literature, but they have been named several times in connection with quadrilateral classifications. Günter Graumann strangely gave these objects two different names in [1, pp. 192, 194]: sloping-kite and sliding-kite. A. Ramachandran called them slant kites in [2, p. 54] and Michael de Villiers called them bisecting quadrilaterals in [3, pp. 19, 206]. The latter is a pretty good name, although a bit confusing: what exactly is bisected?We have found no papers and only two books where any theorems on such quadrilaterals are studied. In each of the books, one necessary and sufficient condition for such quadrilaterals is proved (see Theorem 1 and 2 in the next section). The purpose of this paper is to investigate basic properties ofconvexbisecting quadrilaterals, but we have chosen to give them a slightly different name. Let us first remind the reader that a quadrilateral whose diagonals have equal lengths is called an equidiagonal quadrilateral and one whose diagonals are perpendicular is called an orthodiagonal quadrilateral.

scholarly journals On the stable rank and real rank of group $C^*$-algebras of nilpotent locally compact groups

2005 ◽  
Vol 97 (1) ◽  
pp. 89
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Stable Rank ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Real Rank ◽  
Locally Compact ◽  
C Algebras ◽  
Necessary And Sufficient

It is shown that if $G$ is an almost connected nilpotent group then the stable rank of $C^*(G)$ is equal to the rank of the abelian group $G/[G,G]$. For a general nilpotent locally compact group $G$, it is shown that finiteness of the rank of $G/[G,G]$ is necessary and sufficient for the finiteness of the stable rank of $C^*(G)$ and also for the finiteness of the real rank of $C^*(G)$.

scholarly journals THE GLIMM IDEAL SPACE OF A TWO-STEP NILPOTENT LOCALLY COMPACT GROUP

2001 ◽  
Vol 44 (3) ◽  
pp. 505-526 ◽  
Author(s):  
Eberhard Kaniuth ◽  
William Moran
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Locally Compact ◽  
C Algebra ◽  
Primary 22D25 ◽  
Secondary 22D10 ◽  
Necessary And Sufficient

AbstractFor a two-step nilpotent locally compact group $G$, we determine the Glimm ideal space of the group $C^*$-algebra $C^*(G)$ and its topology. This leads to necessary and sufficient conditions for $C^*(G)$ to be quasi-standard. Moreover, some results about the Glimm classes of points in the primitive ideal space $\mathrm{Prim}(C^*(G))$ are obtained.AMS 2000 Mathematics subject classification: Primary 22D25. Secondary 22D10

scholarly journals On orderability of topological groups

1985 ◽  
Vol 8 (4) ◽  
pp. 747-754
Author(s):  
G. Rangan
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Group Structure ◽  
Locally Compact Abelian Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Groups ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Totally Disconnected

A necessary and sufficient condition for a topological group whose topology can be induced by a total order compatible with the group structure is given and such groups are called ordered or orderable topological groups. A separable totally disconnected ordered topological group is proved to be non-archimedean metrizable while the converse is shown to be false by means of an example. A necessary and sufficient condition for a no-totally disconnected locally compact abelian group to be orderable is also given.

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