English

Planes in Schatten-$3$

Functional Analysis 2022-07-27 v1

Abstract

We prove that any two-dimensional real subspace of Schatten-3 can be linearly isometrically embedded into L3L_{3}. This resolves the case p=3p = 3 of Hanner's inequality for Schatten classes, conjectured by Ball, Carlen and Lieb. We conjecture that similar isometric embedding is possible for any p1p \geq 1.

Keywords

Cite

@article{arxiv.2207.12812,
  title  = {Planes in Schatten-$3$},
  author = {Otte Heinävaara},
  journal= {arXiv preprint arXiv:2207.12812},
  year   = {2022}
}

Comments

13 pages

R2 v1 2026-06-25T01:14:09.706Z