English

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.

Keywords

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

R2 v1 2026-06-23T17:58:11.037Z