Lp spaces of operator-valued functions

Ramsey, Christopher; Reeves, Adam

Lp spaces of operator-valued functions

Author

Ramsey, Christopher

Reeves, Adam

Date

2021

Keywords

positive operator-valued measure, POVM, quantum random variable, operator-valued integration, Schatten norm, decomposable norm

Abstract (summary)

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 Lp 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.

Publication Information

Ramsey, C. & Reeves, A. (2021). "Lp spaces of operator-valued functions". arXiv:2008.08569. https://doi.org/10.48550/arXiv.2008.08569

DOI

https://doi.org/10.48550/arXiv.2008.08569

Item Type

Article

Rights

Attribution-NonCommercial (CC BY-NC)