L$^p$ spaces of operator-valued functions
Functional Analysis
2021-08-31 v2
Abstract
We define a p-norm in the context of quantum random variables, measurable operator-valued functions with respect to a positive operator-valued measure. This norm leads to a operator-valued L^p space that is shown to be complete. Various other norm candidates are considered as well as generalizations of H\"older's inequality to this new context.
Cite
@article{arxiv.2008.08569,
title = {L$^p$ spaces of operator-valued functions},
author = {Christopher Ramsey and Adam Reeves},
journal= {arXiv preprint arXiv:2008.08569},
year = {2021}
}
Comments
15 pages, final version, accepted to Integral Equations and Operator Theory