Topological algebras of locally solid vector subspaces of order bounded\n operators

2016/11/04 by Omid Zabeti, Zabeti, Omid
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1611.01494

openalex publication_date 2016/11/04 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Let E be a locally solid vector lattice. In this paper, we consider two\nparticular vector subspaces of the space of all order bounded operators on E.\nWith the aid of two appropriate topologies, we show that under some conditions,\nthey establish both, locally solid vector lattices and topologically complete\ntopological algebras.\n

Related

• Topological algebras of bounded operators with locally solid Riesz spaces
• Spaces of uτ-Dunford-Pettis and uτ-Compact Operators on Locally Solid Vector Lattices
• The oτ-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces
• uτ-continuous operators on locally solid vector lattices
• AM-spaces from a locally solid vector lattice point of view with applications