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.
@article{IVM_2016_5_a4,
author = {A. M. Bikchentaev},
title = {On operator monotone and operator convex functions},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {70--74},
publisher = {mathdoc},
number = {5},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2016_5_a4/}
}
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/