# Reflexivity and non-weakly null maximizing sequences

## TL;DR

This paper introduces a new reflexivity-related property crucial for understanding norm attaining operators, with applications to compact perturbations and characterizations of certain polynomials on Hilbert spaces.

## Contribution

It presents a novel property linked to reflexivity that advances the characterization of norm attaining operators and applies it to operator perturbations and polynomial analysis.

## Key findings

- New reflexivity property related to norm attaining operators
- Characterization of norm attaining scalar-valued 2-homogeneous polynomials on ℓ₂
- Application to compact perturbations of linear operators

## Abstract

We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize norm attaining scalar-valued continuous $2$-homogeneous polynomials on $\ell_{2}$.