Classifying the closed ideals of bounded operators on two families of non-separable classical Banach spaces

TL;DR

This paper classifies the structure of closed ideals of bounded operators on two specific non-separable Banach spaces, expanding understanding of operator ideals in complex infinite-dimensional settings.

Contribution

It provides a complete classification of closed ideals of bounded operators on certain non-separable Banach spaces involving direct sums and uncountable cardinals.

Findings

Classification of closed ideals for the spaces considered.

Extension of ideal classification to non-separable spaces.

Results applicable to spaces with uncountable cardinality.

Abstract

We classify the closed ideals of bounded operators acting on the Banach spaces $\left(\bigoplus_{n \in \mathbb{N}} \ell_2^n\right)_{c_0} \oplus c_0(\Gamma)$ and $\left(\bigoplus_{n \in \mathbb{N}} \ell_2^n\right)_{\ell_1} \oplus \ell_1(\Gamma)$ for every uncountable cardinal $\Gamma$.