2018/11/22 by Gustavo Araújo, Araújo, Gustavo, Joedson Santos +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1811.09183
openalex publication_date 2018/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A famous theorem due to Maurey and Pisier asserts that for an infinite dimensional Banach space E, the infumum of the q such that the identity map idE is absolutely ( q,1) -summing is precisely \cot E. In the same direction, the Dvoretzky--Rogers Theorem asserts idE fails to be absolutely ( p,p) -summing, for all p≥1. In this note, among other results, we unify both theorems by charactering the parameters q and p for which the identity map is absolutely ( q,p)-summing. We also provide a result that we call strings of coincidences that characterize a family of coincidences between classes of summing operators. We illustrate the usefulness of this result by extending classical result of Diestel, Jarchow and Tonge and the coincidence result of Kwapień.