Jensen’s inequality for spectral order and submajorization

JORGE ANTEZANA; PEDRO MASSEY; DEMETRIO STOJANOFF

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ELSEVIER

Año: 2007 vol. 331 p. 297 - 307

0022-247X

Let A be a C*-algebra and P :A-->L(H) be a positive unital map. Then, for a convex function  f: I--> R defined on some open interval I and a self-adjoint element a in A whose spectrum lies in I , we obtain a Jensen´s-type inequality P(f(a)) >> ƒ(P (a)) where ">>"  denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., operator convex, monotone convex or arbitrary convex functions. Some extensions of Jensen´s-type inequalities to the multi-variable case are considered.