On quotients of Banach spaces having shrinking unconditional bases

1990/11/16 by Edward Odell, Odell, Edward
Mathematics · #46B #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9201219

openalex publication_date 1990/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that if a Banach space Y is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in Y has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is c_o-saturated.

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• New examples of c₀-saturated Banach spaces II
• On Schreier unconditional sequences
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• Partial Unconditionality
• Asymptotic Unconditionality