Topics in Contemporary Mathematical Analysis and Applications

5 Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices

Abdullah Aydin

Muş Alparslan University

CONTENTS

5.1     Introduction

5.2     Preliminaries

5.3     p_τ-Continuous and p_τ-Bounded Operators

5.4     up_τ-Continuous Operators

5.5     The Compact-Like Operators

Bibliography

5.1     Introduction

Lattice-valued norms on vector lattices play an important and effective role in the functional analysis. It is well known that order convergence in vector lattice is not topological unless dimension is finite. However, thanks to the order convergence, some properties like order continuous in vector lattice can be defined. We refer the reader for an exposition on basic notions and properties of vector lattice (or, Riesz space) to ...