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

2018/11/10 by Omid Zabeti, Zabeti, Omid
Mathematics · #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1811.04296

openalex publication_date 2018/11/10 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

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

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