Statistical unbounded convergence in Banach lattices

TL;DR

This paper explores statistical unbounded order and topology convergence in Banach lattices, characterizing key properties of these spaces through new convergence concepts.

Contribution

It introduces and analyzes statistical unbounded convergence in Banach lattices, linking it to classical properties like order continuity and reflexivity.

Findings

Characterizes order continuous Banach lattices via statistical unbounded convergence.

Establishes relationships between statistical unbounded convergence and KB, reflexive Banach lattices.

Provides new insights into convergence behavior in Riesz spaces.

Abstract

Several recent papers investigated unbounded and statistical versions of order convergence and topology convergence in locally solid Riesz space. In this papers, we study the statistical unbounded order and topology convergence in Riesz spaces and Banach lattices. In particular, we study the relationship of those convergence and characterize order continuous, KB, reflexive Banach lattices in terms of these convergence.