Fredholm multiplication conditional type operators on L^p-spaces

TL;DR

This paper studies the properties of multiplication conditional type operators on L^p-spaces, focusing on their closed range and Fredholm characteristics, especially in non-atomic measure spaces, supported by examples.

Contribution

It provides a characterization of Fredholm multiplication conditional type operators on L^p-spaces over non-atomic measure spaces, extending understanding of their functional analysis properties.

Findings

Characterization of closed range multiplication conditional type operators

Criteria for Fredholm operators in non-atomic measure spaces

Examples illustrating the theoretical results

Abstract

In this paper, first we investigate closed range multiplication conditional type operators between two Lp-spaces. Then we characterize Fredholm ones when the underlying measure space is non-atomic. Finally we give some examples.