Lp spaces of operator-valued functions
positive operator-valued measure, POVM, quantum random variable, operator-valued integration, Schatten norm, decomposable norm
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.
Ramsey, C. & Reeves, A. (2021). "Lp spaces of operator-valued functions". arXiv:2008.08569. https://doi.org/10.48550/arXiv.2008.08569
Attribution-NonCommercial (CC BY-NC)