Separating bounded group homomorphisms on ℓ-groups of functions

Suppose X is a topological ring. It is known that there are three classes of bounded group homomorphisms on X whose topological structures make them again topological rings. First, we show that if X is a Hausdorff topological ring, then so are these classes of bounded group homomorphisms on X. Now, assume that X is a locally solid lattice ring. In this paper, our aim is to consider lattice structure on these classes of bounded group homomorphisms more precisely, we show that, under some mild assumptions, they are locally solid lattice rings. In fact, we consider bounded order bounded homomorphisms on X. Then we show that under the assumed topology, they form locally solid lattice rings. For this reason, we need a version of the remarkable RieszKantorovich formulae for order bounded operators in Riesz spaces in terms of order bounded homomorphisms on topological lattice groups.

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Ghanaian Migrants in Germany and the Social Construction of Diaspora Les migrants ghanéens en Allemagne et la construction sociale de la diaspora

African Diaspora ◽

10.1163/187254608x346051 ◽

2008 ◽

Vol 1 (1-2) ◽

pp. 28-52 ◽

Cited By ~ 15

Author(s):

Boris Nieswand

Keyword(s):

Social Construction ◽

Theoretical Concept ◽

Web Pages ◽

Nation State ◽

Hometown Associations ◽

The Social ◽

Bounded Group ◽

Different Types ◽

Newspaper Articles

Abstract This article explores diasporic discourses and practices among Ghanaian migrants in Germany. Instead of presuming that 'diaspora' is a stringent theoretical concept or refers to a bounded group in a sociological sense, it is argued that it provides migrants with a grammar of practice that allows for the situational and contextual construction of different types of 'diasporas'. Empirically, three social sites of construction are identified. Firstly, the Ghanaian nation-state and the reconfiguration of Ghanaian nationalism play an important role for promoting diasporic discourses. Secondly, the discourse of development and 'charity rituals' of ethnic and 'hometown' associations are of particular relevance for the proliferation of Ghanaian 'diasporas'. Thirdly, Ghanaian chieftaincies are involved in diasporic activities. The article is based on data collected in thirteen months of multi-sited ethnography conducted in Germany and Ghana between 2001 and 2003 and the analysis of video tapes, newspaper articles and web pages. Cet article explore les discours diasporiques et les pratiques trouvées parmi les migrants ghanéens en Allemagne. Plutôt que de présumer que la « diaspora » est un concept théorique strict ou fait référence à un groupe délimité dans un sens sociologique, il est soutenu qu'il fournit une grammaire de pratiques qui permet la construction situationnelle et contextuelle de différents types de « diasporas ». Empiriquement, trois lieux de construction sociale sont identifiés. Premièrement l'Etat-nation ghanéen et la reconfiguration du nationalisme ghanéen jour un rôle important pour promouvoir des discours diasporiques. Deuxièmement, le discours du développement et des « rituels de charité » des associations ethniques et des « villes natales » a une pertinence particulière pour la prolifération des « diasporas » ghanéennes. Troisièmement, les chefferies des tribus ghanéennes sont impliquées dans les activités de la diaspora. Empiriquement, cet article se base sur treize mois d'ethnographie, conduite en Allemagne et au Ghana entre 2001 et 2003, et sur l'analyse de bandes-vidéos, d'articles de journaux et de sites web.

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A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

Filomat ◽

10.2298/fil2009897z ◽

2020 ◽

Vol 34 (9) ◽

pp. 2897-2905

Author(s):

Omid Zabeti

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Lattice Structures ◽

Fatou Property ◽

Topological Structures ◽

Lattice Group ◽

Topological Lattice ◽

Bounded Group ◽

Different Types ◽

Necessary And Sufficient

Suppose G is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on G which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for completeness of different types of bounded group homomorphisms between topological rings have been obtained, as well.

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Errata to the paper "On exact sequences and strict bounded group homomorphisms "

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.48379 ◽

2022 ◽

Vol 40 ◽

pp. 1-1

Author(s):

Dinamérico Pereira Pombo Junior

Keyword(s):

Bounded Group ◽

Exact Sequences

Corrections to the above-mentioned paper are provided.

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Some properties of o-bounded and strictly o-bounded groups

Applied General Topology ◽

10.4995/agt.2000.3022 ◽

2000 ◽

Vol 1 (1) ◽

pp. 29 ◽

Cited By ~ 13

Author(s):

C. Hernández ◽

M. Tkachenko ◽

D. Robbie

Keyword(s):

Topological Group ◽

Topological Groups ◽

Bounded Group

<p>We continue the study of (strictly) o-bounded topological groups initiated by the first listed author and solve two problems posed earlier. It is shown here that the product of a Comfort-like topological group by a (strictly) o-bounded group is (strictly) o-bounded. Some non-trivial examples of strictly o-bounded free topological groups are given. We also show that o-boundedness is not productive, and strict o-boundedness cannot be characterized by means of second countable continuous homomorphic images.</p><p> </p>

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Low-dimensional bounded cohomology and extensions of groups

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-114969 ◽

2020 ◽

Vol 126 (1) ◽

pp. 5-31

Author(s):

Nicolaus Heuer

Keyword(s):

Group Cohomology ◽

The Other ◽

Bounded Cohomology ◽

Seminal Paper ◽

Bounded Group ◽

Dimension 2 ◽

Low Dimensional ◽

Positively Curved ◽

Funct Anal ◽

Cohomology Of Groups

Bounded cohomology of groups was first studied by Gromov in 1982 in his seminal paper M. Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic “non-positively curved” groups. On the other hand, there is a well-known interpretation of ordinary group cohomology in dimension $2$ and $3$ in terms of group extensions. The aim of this paper is to make this interpretation available for bounded group cohomology. This will involve quasihomomorphisms as defined and studied by K. Fujiwara and M. Kapovich, On quasihomomorphisms with noncommutative targets, Geom. Funct. Anal. 26 (2016), no. 2, 478–519.

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2. Non-unitarizable uniformly bounded group representations

Lecture Notes in Mathematics - Similarity Problems and Completely Bounded Maps ◽

10.1007/978-3-540-44563-0_3 ◽

2001 ◽

pp. 31-57

Author(s):

Gilles Pisier

Keyword(s):

Group Representations ◽

Bounded Group ◽

Uniformly Bounded

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