Non-commutative differentiation and estimates on operator integrals

Master thesis (2021)

Authors

L.M. Janssen Electrical Engineering, Mathematics and Computer Science

Contributors

M.P.T. Caspers Analysis - EEMCS (supervisor 1)
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS (supervisor 2)
J.M.A.M. van Neerven Analysis - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Luc Janssen
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Published Date

28-06-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In 2017 Martijn Caspers, Fedor Sukochev and Dmitriy Zanin published a paper which generalises the proof of Davies' 1988 paper, and thus resolves the Nazarov-Peller conjecture. The proofs of these papers have been presented in this thesis. They have been expanded with a proof that generalises the conjecture to arbitrary Schatten classes. The optimality of the estimates in the conjecture is also studied, following the example of the 2016 paper by Coine et al. In addition, the quantum mechanical context is provided to interpret the presented results.