Fredholmness and Weylness of block operator matrices

TL;DR

This paper characterizes Fredholmness and Weylness of upper triangular block operator matrices of arbitrary dimension in infinite-dimensional Hilbert spaces, extending previous results and removing the separability assumption.

Contribution

It provides new characterization results for Fredholmness and Weylness of block operator matrices without assuming separability, generalizing prior work to arbitrary dimensions.

Findings

Extended known results to arbitrary dimension n.

Characterized Fredholmness and Weylness without separability.

Improved perturbation results for infinite-dimensional spaces.

Abstract

This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus extending some known results from Cao X. et al. (2006, 2005) and Zhang et al. (2012) to the case of arbitrary dimension n. We pose our results without using separability assumption, thus improving perturbation results from Wu X. et al. (2020).