Frechet differentiability of Sp norms

2013/06/03 by Denis Potapov, Fedor Sukochev, Potapov, Denis +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1306.0362

openalex publication_date 2013/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question in the affirmative. A key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of L.S. Koplienko's conjecture concerning existence of higher order spectral shift functions.

Cited by

• On the differentiability of the Sobolev norm of W^k,1(M) on compact Riemannian manifolds

Related

• Spectral shift for relative Schatten class perturbations
• Higher-order spectral shift function for resolvent comparable perturbations
• Spectral shift function of higher order
• Trace formulas in higher dimensions
• Higher order \Sc²-differentiability and application to Koplienko trace formula