Viewing *-multiplication operators between Orlics spaces

TL;DR

This paper characterizes Lambert multipliers between Orlicz spaces, explores conditions for *-multiplication operators to have closed range, and investigates when such operators are Fredholm, advancing understanding of operator behavior in Orlicz spaces.

Contribution

It provides new characterizations and necessary conditions for *-multiplication operators in Orlicz spaces, including closed range and Fredholm properties.

Findings

Lambert multipliers characterized via conditional expectation operators

Necessary and sufficient conditions for closed range of *-multiplication operators

Conditions under which *-multiplication operators are Fredholm

Abstract

In this paper, Lambert multipliers acting between Orlicz spaces are characterized based on conditional expectation operators. Also, we give necessary and sufficient conditions to *-multiplication operators to be closed range. Finally, the necessary condition under which a *-multiplication operator to be Fredholm operator is investigated.