# Finite sum of weighted composition operators with closed range

## TL;DR

This paper characterizes when finite sums of weighted composition operators have closed ranges between different Lp-spaces, and explores their polar decomposition and invertibility properties.

## Contribution

It provides new characterizations of closedness, invertibility, and polar decomposition for finite sums of weighted composition operators between Lp-spaces.

## Key findings

- Closedness of the range characterized for finite sums
- Conditions for invertibility established
- Polar decomposition formulas derived

## Abstract

In this paper, first we characterize closedness of range of the finite sum of weighted composition operators between different Lp-spaces. Then we discuss polar decomposition and invertibility of these operators.