Spaces of uτ-Dunford-Pettis and uτ-Compact Operators on Locally Solid Vector Lattices

2017/10/31 by Nazife Erkurşun-Özcan, Ozcan, Nazife Erkursun, Niyazi Anıl Gezer +3
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1710.11434

openalex publication_date 2017/10/31 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Suppose X is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on X. In this paper, we consider some situations under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of uaw-Dunford-Pettis operators and uaw-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between topological and lattice structures of these operators. In particular, we characterize those spaces for which these concepts of operators and the corresponding classes of bounded ones coincide.

Related

• Topological algebras of locally solid vector subspaces of order bounded\n operators
• uτ-continuous operators on locally solid vector lattices
• The Krengel's theorem for compact operators between locally solid vector lattices
• Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices
• The oτ-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces