Planes in Schatten-$3$

Otte Heinävaara

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arXiv · 2207.12812

Planes in Schatten-$3$

Otte Heinävaara

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Abstract

We prove that any two-dimensional real subspace of Schatten-3 can be linearly isometrically embedded into $L_{3}$. This resolves the case $p = 3$ of Hanner's inequality for Schatten classes, conjectured by Ball, Carlen and Lieb. We conjecture that similar isometric embedding is possible for any $p \geq 1$.

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BibTeX RIS

Otte Heinävaara. 2022-07-26. Planes in Schatten-$3$. https://arxiv.org/abs/2207.12812

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