Separate continuity of the Lempert function of the spectral ball

TL;DR

This paper characterizes all matrices within the spectral unit ball for which the Lempert function remains continuous, advancing understanding of complex geometric properties in spectral domains.

Contribution

It provides a complete characterization of matrices in the spectral ball with continuous Lempert functions, a novel result in spectral geometry.

Findings

Identifies matrices with continuous Lempert functions in the spectral ball

Advances understanding of complex geometric properties in spectral domains

Provides a complete classification of such matrices

Abstract

We find all matrices $A$ from the spectral unit ball $\Omega_n$ such that the Lempert function $l_{\Omega_n}(A,\cdot)$ is continuous.