Hokkaido University (Emeritus), Shiroishi-ku, Hongo-dori 9, Minami 4-10-805, Sapporo 003-0024, Japan
Copyright © 2010 Tsuyoshi Ando. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its
convexity by the following trace-inequalities:
A related topic will be also discussed.