Geodesic
On operator monotone and operator convex functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 70-74

Voir la notice de l'article provenant de la source Math-Net.Ru

We establish monotonicity and convexity criteria for a continuous function $f\colon\mathbb R^+\to\mathbb R$ with respect to any $C^*$-algebra. We obtain some estimates for noncompactness measure of $W^*$-algebra elements products differences. We also give a commutativity criterion for a positive $\tau$-measurable operator and a positive operator from a von Neumann algebra.
Keywords: Hilbert space, von Neumann algebra, $C^*$-algebra, $W^*$-algebra, operator monotone function, operator convex function, measure of noncompactness, trace, measurable operator, commutativity of operators. 
A. M. Bikchentaev. On operator monotone and operator convex functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 70-74. http://geodesic.mathdoc.fr/item/IVM_2016_5_a4/
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