Jensen's inequality for spectral order and submajorization
Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an...
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| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2007
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83285 |
| Aporte de: |
| Sumario: | Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ 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 Jensen's-type inequalities to the multi-variable case are considered. |
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