# Compact operators under Orlicz functions

## TL;DR

This paper introduces noncommutative Orlicz sequence spaces, explores their properties, and applies these concepts to compute traces and norms of Toeplitz operators on the Bergman space.

## Contribution

It defines noncommutative Orlicz sequence spaces, establishes their reflexivity criteria, and applies the theory to Toeplitz operators, linking operator theory with noncommutative Orlicz spaces.

## Key findings

- Defined noncommutative Orlicz sequence spaces
- Established reflexivity criteria for these spaces
- Computed trace and norm of Toeplitz operators

## Abstract

In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these spaces. At last, as an application, we find the Toeplitz operator on the Bergman space belongs to some noncommutative Orlicz sequence spaces, hence the trace and the norm of operator could be computed.