von Neumann's trace inequality for Hilbert–Schmidt operators

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Abstract

von Neumann's inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Hilbert–Schmidt class, Inequalities on singular values, Trace inequality
Original languageEnglish
Pages (from-to)149-157
JournalExpositiones Mathematicae
Volume39
Issue number1
Early online date2020
Publication statusPublished - 2021
Publication categoryResearch
Peer-reviewedYes