(Co-)type and the linear stability of Wigner's symmetry theorem

2019/07/12 by Javier Cuesta, Cuesta, Javier
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1907.05733

openalex publication_date 2019/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the relation between the linear stability of almost-symmetries and the geometry of the Banach spaces on which these transformations are defined. We show that any transformation between finite dimensional Banach spaces that preserves transition probabilities up to an additive error admits an approximation by a linear map, and the quality of the approximation depends on the type and cotype constants of the involved spaces.

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