L spaces of operator-valued functions
arXiv:2008.08569
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 Hölder's inequality to this new context.
15 pages, final version, accepted to Integral Equations and Operator Theory