# Compactification, and beyond, of composition operators on Hardy spaces by weights

## TL;DR

This paper investigates how multiplying by weights affects the compactness and Schatten class membership of composition operators on Hardy spaces, exploring conditions under which these properties are altered.

## Contribution

It provides new criteria for when weights can change the compactness and Schatten class status of composition operators on Hardy spaces.

## Key findings

- Multiplication by weights can turn non-compact operators into compact ones.
- Conditions for weights to place operators in Schatten classes are established.
- Analysis of when compact operators become non-compact through weights.

## Abstract

We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can turn a compact composition operator into a non-compact one. MSC 2010 primary: 47B33 ; secondary: 46B28