Planes in Schatten-3
Abstract
We prove that any two-dimensional real subspace of Schatten-3 can be linearly isometrically embedded into L3. 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 ≥ 1.
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