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Trace-Inequalities and Matrix-Convex Functions

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Author(s): Ando Tsuyoshi

Journal: Fixed Point Theory and Applications
ISSN 1687-1820

Volume: 2010;
Issue: 1;
Start page: 241908;
Date: 2010;
Original page

ABSTRACT
Abstract 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: for . A related topic will be also discussed.
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