Weakly and weak$^\ast$ $p$-convergent operators

TL;DR

This paper introduces and analyzes classes of weakly p-convergent and weak* p-convergent operators between locally convex spaces, exploring their properties, relationships, and characterizations.

Contribution

It extends the concept of weakly p-convergent operators from Banach spaces to locally convex spaces, providing new characterizations and establishing their ideal properties.

Findings

Established relationships between the classes of operators.

Proved that these classes have ideal properties.

Provided numerous characterizations of the operators.

Abstract

Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators are given.