Descriptive set theoretic methods applied to strictly singular and strictly cosingular operators

2008/05/31 by George Androulakis, Androulakis, G., Kevin Beanland +1
Mathematics · #47A15 #47B07 #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.0806.0056

openalex publication_date 2008/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The class of strictly singular operators originating from the dual of a separable Banach space is written as an increasing union of ω₁ subclasses which are defined using the Schreier sets. A question of J. Diestel, of whether a similar result can be stated for strictly cosingular operators, is studied.

Citations

• Complexity of weakly null sequences

Related

• Quantifications of strictly singular operators and strictly cosingular operators
• Banach lattice versions of strict singularity
• Strictly singular operators on the Baernstein and Schreier spaces
• Strictly Singular Uniform λ-Adjustment in Banach Spaces
• An Ordinal Index on the Space of Strictly Singular Operators