Operator inequalities of Jensen type
| Autor: | Moslehian, M. S., Micic, J., Kian, M. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Top. Algebra Appl. 1 (2013), 9-21 |
| Druh dokumentu: | Working Paper |
| Popis: | We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if $f:[0,\infty) \to \mathbb{R}$ is a continuous convex function with $f(0)\leq 0$, then {equation*} \sum_{i=1}^{n} f(C_i) \leq f(\sum_{i=1}^{n}C_i)-\delta_f\sum_{i=1}^{n}\widetilde{C}_i\leq f(\sum_{i=1}^{n}C_i) {equation*} for all operators $C_i$ such that $0 \leq C_i\leq M \leq \sum_{i=1}^{n} C_i $ \ $(i=1,...,n)$ for some scalar $M\geq0$, where $ \widetilde{C_i} = 1/2 - |\frac{C_i}{M}- 1/2 |$ and $\delta_f = f(0)+f(M) - 2 f(\frac{M}{2})$. Comment: 17 pages, to appear in Topological Algebra and its Applications (a newly established journal by Versita Ltd.)) |
| Databáze: | arXiv |
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