Type and Cotype Constants and the Linear Stability of Wigner’s Symmetry Theorem

Abstract

We study the relation between almost-symmetries and the geometry of Banach spaces. We show that any almost-linear extension of a transformation 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.

Keywords

• Wigner’s theorem
• stability
• almost-symmetry
• almost-linear
• type
• cotype
• Banach spaces