Positivity

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A property of conditional expectation

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Abstract

Let \(({\mathcal {M}},\tau )\) be a semi-finite von Neumann algebra, \(({\mathcal {N}},\tau |_{{\mathcal {N}}})\) be a semi-finite von Neumann subalgebra and \({\mathcal {E}}:\;{\mathcal {M}}\rightarrow {\mathcal {N}}\) be a conditional expectation which leaves \(\tau \) invariant. We proved super-majorization for the conditional expectation \({\mathcal {E}}\) and related inequalities.

Keywords

Conditional expectation Super-majorization Semifinite von Neumann algebra 

Mathematics Subject Classification

46L52 47L05 

Notes

Acknowledgements

We thank F. A. Sukochev for suggesting (pointing out) Remark 1. We also thank the referee for very useful comments, which improved the paper. The authors are partially supported by NSFC Grant No. 11771372.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityÜrümqiChina

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