Jensen's Operator Inequality
Operator Algebras
2007-05-23 v1 Spectral Theory
Abstract
We establish what we consider to be the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval. This is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions used in earlier versions of the theory. As a consequence, we no longer need to impose conditions on the interval of definition. We show how this relates to the pinching inequality of Davis, and how Jensen's trace inequlity generalizes to C*-algebras..
Keywords
Cite
@article{arxiv.math/0204049,
title = {Jensen's Operator Inequality},
author = {Frank Hansen and Gert K. Pedersen},
journal= {arXiv preprint arXiv:math/0204049},
year = {2007}
}
Comments
12 pp