L$^p$ spaces of operator-valued functions

Christopher Ramsey; Adam Reeves

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arXiv · 2008.08569

L$^p$ spaces of operator-valued functions

Christopher Ramsey·Adam Reeves

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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.

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Christopher Ramsey, Adam Reeves. 2020-08-19. L$^p$ spaces of operator-valued functions. https://arxiv.org/abs/2008.08569

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