IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Jensen's inequality for spectral order and submajorization
Autor/es:
JORGE ANTEZANA; PEDRO MASSEY; DEMETRIO STOJANOFF
Revista:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Referencias:
Año: 2007 p. 297 - 297
ISSN:
0022-247X
Resumen:
Let $mathcal{A}$ be a $C^*$-algebra and $phi:cA ightarrow L(H)$ be a positive unital map. Then, for a convex function $f:I ightarrow mathbb{R}$ defined on some open interval and a self-adjoint element $ain mathcal{A}$ whose spectrum lies in $I$, we obtain a JensenĀ“s-type inequality $f(phi(a)) leq phi(f(a))$ where $le$ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered i.e.,  monotone convex or arbitrary convex functions. Some extensions of JensenĀ“s-type inequalities to the multi-variable case are considered.