From Matrix to Operator Inequalities
Operator Algebras
2019-08-15 v1 Functional Analysis
Abstract
We generalize Loewner's method for proving that matrix monotone functions are operator monotone. The relation x \leq y on bounded operators is our model for a definition for C*-relations of being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved, and verify a technical condition, then such a theorem will follow from its restriction to matrices. Applications are shown regarding norms of exponentials, the norms of commutators and "positive" noncommutative *-polynomials.
Cite
@article{arxiv.0902.0102,
title = {From Matrix to Operator Inequalities},
author = {Terry A. Loring},
journal= {arXiv preprint arXiv:0902.0102},
year = {2019}
}
Comments
12 pages