Lp spaces of operator-valued functions

Author
Ramsey, Christopher
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
Article