von Neumann's trace inequality for Hilbert–Schmidt operators

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von Neumann's trace inequality for Hilbert–Schmidt operators. / Carlsson, Marcus.

In: Expositiones Mathematicae, Vol. 39, No. 1, 2021, p. 149-157.

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TY - JOUR

T1 - von Neumann's trace inequality for Hilbert–Schmidt operators

AU - Carlsson, Marcus

PY - 2021

Y1 - 2021

N2 - 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”.

AB - 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”.

KW - Hilbert–Schmidt class

KW - Inequalities on singular values

KW - Trace inequality

UR - http://www.scopus.com/inward/record.url?scp=85087126153&partnerID=8YFLogxK

U2 - 10.1016/j.exmath.2020.05.001

DO - 10.1016/j.exmath.2020.05.001

M3 - Article

AN - SCOPUS:85087126153

VL - 39

SP - 149

EP - 157

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

SN - 0723-0869

IS - 1

ER -