Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic

2024/01/29 by Hùng Việt Chu, Thomas Schlumprecht, Chu, Hung Viet +1
Mathematics · #46B06 #46B20 (primary) #46B25 (secondary) #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2401.16491

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every countable ordinal ξ, the Tsirelson's space T_ξ of order ξ, is naturally, i.e., via the identity, 3-isomorphc to its modified version. For the first step, we prove that the Schreier family S_ξ is the same as its modified version S^M_ξ, thus answering a question by Argyros and Tolias. As an application, we show that the algebra of linear bounded operators on T_ξ has 2^{\mathfrak c} closed ideals.

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