Frechet differentiability of Sp norms
Operator Algebras
2013-06-04 v1 Functional Analysis
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.
Cite
@article{arxiv.1306.0362,
title = {Frechet differentiability of Sp norms},
author = {Denis Potapov and Fedor Sukochev},
journal= {arXiv preprint arXiv:1306.0362},
year = {2013}
}