von Neumann's trace inequality for Hilbert–Schmidt operators

• 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”.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Hilbert–Schmidt class

Inequalities on singular values

Trace inequality

Publication and Content Type

art (subject category)

ref (subject category)