# Characterization of Absolutely Norm Attaining Compact Hyponormal Operators

## TL;DR

This paper characterizes when compact hyponormal operators on infinite-dimensional Hilbert spaces are absolutely norm attaining, providing necessary and sufficient conditions and exploring their structure and properties.

## Contribution

It offers a complete characterization of absolutely norm-attaining compact hyponormal operators, including conditions and structural insights, advancing understanding in operator theory.

## Key findings

- Necessary and sufficient conditions for absolute norm attainability.
- Structural analysis of self-adjoint and normal compact hyponormal operators.
- Properties of operators and their commutators when absolutely norm attaining.

## Abstract

In this paper, we characterize absolute norm-attainability for compact hyponormal operators. We give necessary and sufficient conditions for a bounded linear compact hyponormal operator on an infinite dimensional complex Hilbert space to be absolutely norm attaining. Moreover, we discuss the structure of compact hyponormal operators when they are self-adjoint and normal. Lastly, we discuss in general, other properties of compact hyponormal operators when they are absolutely norm attaining and their commutators.