The Schatten p-quasinorm on Euclidean Jordan algebras

Abstract

In this article, we proved that a Schatten $ p $-(quasi)norm for $ 0 < p < 1 $, defined on Euclidean Jordan algebras, satisfied a relaxed triangle inequality with an optimal constant $ 2^{\frac{1}{p} - 1} $; hence, it indeed induced a quasinorm. This confirmed the validity of a conjecture raised by Huang, Chen, and Hu.

Keywords

• schatten $ p $-quasinorm
• euclidean jordan algebra
• spectral function
• majorization