
TL;DR
This paper proves that any two-dimensional subspace of Schatten-3 space can be isometrically embedded into L3, resolving a specific case of Hanner's inequality and suggesting broader possibilities for p ≥ 1.
Contribution
It establishes the isometric embedding for Schatten-3 spaces, solving a conjecture for p=3 and proposing a generalization for all p ≥ 1.
Findings
Confirmed isometric embedding for Schatten-3 into L3
Resolved the p=3 case of Hanner's inequality for Schatten classes
Proposed conjecture for embeddings for all p ≥ 1
Abstract
We prove that any two-dimensional real subspace of Schatten-3 can be linearly isometrically embedded into . This resolves the case of Hanner's inequality for Schatten classes, conjectured by Ball, Carlen and Lieb. We conjecture that similar isometric embedding is possible for any .
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematics and Applications · Finite Group Theory Research
