The Hölder continuity of Löwner’s operator in Euclidean Jordan algebras

Abstract

Lowner’s operator in Euclidean Jordan algebras, defined via the spectral decomposition of the elements of a scalar function, has been widely used in various optimization problems over Euclidean Jordan algebras. In this note, we shall show that Lowner’s operator in Euclidean Jordan algebras is Holder continuous if and only if the underlying scalar function is Holder continuous. Such a property will be useful in designing solution methods for symmetric cone programming and symmetric cone complementarity problem.