Operator Connections and Borel Measures on the Unit Interval
Functional Analysis
2012-11-08 v1
Abstract
A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the joint-continuity from above. A mean is a normalized connection. In this paper, we show that there is a one-to-one correspondence between connections and finite Borel measures on the unit interval via a suitable integral representation. Every mean can be regarded as an average of weighted harmonic means. Moreover, we investigate decompositions of connections, means, symmetric connections and symmetric means.
Cite
@article{arxiv.1211.1465,
title = {Operator Connections and Borel Measures on the Unit Interval},
author = {Pattrawut Chansangiam and Wicharn Lewkeeratiyutkul},
journal= {arXiv preprint arXiv:1211.1465},
year = {2012}
}
Comments
12 pages