The $p$-Gelfand Phillips Property in Spaces of Operators and Dunford-Pettis like sets

TL;DR

This paper investigates the $p$-Gelfand Phillips property in operator spaces and explores Dunford-Pettis like sets in Banach spaces, focusing on conditions under which $p$-convergent operators are weakly compact.

Contribution

It introduces new insights into the $p$-Gelfand Phillips property in operator spaces and characterizes Banach spaces where $p$-convergent operators are weakly compact.

Findings

Characterization of Banach spaces with the property that all $p$-convergent operators are weakly compact.

Analysis of Dunford-Pettis like sets in Banach spaces.

Extension of the $p$-Gelfand Phillips property to spaces of operators.

Abstract

The $p$-Gelfand Phillips property ($1\le p<\infty$) is studied in spaces of operators. Dunford - Pettis type like sets are studied in Banach spaces. We discuss Banach spaces $X$ with the property that every $p$-convergent operator $T:X\to Y$ is weakly compact, for every Banach space $Y$.