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\(\hbox {L}^p\) Spaces of Operator-Valued Functions

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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 Hölder’s inequality to this new context.

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Acknowledgements

The first author was supported by NSERC Discovery Grant 2019-05430. The second author was partially supported by MacEwan University USRI-Project grants. Both authors would like to thank the reviewer for his/her insightful comments and corrections.

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Correspondence to Christopher Ramsey.

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Ramsey, C., Reeves, A. \(\hbox {L}^p\) Spaces of Operator-Valued Functions. Integr. Equ. Oper. Theory 93, 54 (2021). https://doi.org/10.1007/s00020-021-02669-x

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  • DOI: https://doi.org/10.1007/s00020-021-02669-x

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