functional analysis

Tingley's Problem for Schatten \(p\)-Classes,

arXiv:2607.11244

summary

The authors prove that any surjective isometry between the unit spheres of Schatten‑von Neumann classes C_p extends to a linear (or conjugate‑linear) isometry of the whole space, resolving Tingley’s problem for all 0 < p ≠ 2 < ∞.

Abstract

We give an affirmative answer to Tingley's problem for Schatten--von Neumann classes by a unified approach for all , extending results due to Fernández-Polo et al.

Topics & keywords

#tingley's problem#schatten p-classes#banach spaces#isometries#operator theoryTingley's problemSchatten–von Neumann classC_pisometric extensionBanach space theory
Tingley's Problem for Schatten \(p\)-Classes, $0<p\ne 2<\infty$ · wovepaper