Isometric embeddings of Banach spaces under optimal projection constants

2020/12/20 by Cleon S. Barroso, Barroso, Cleon S.
Computer Science · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2012.10849

openalex publication_date 2020/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a Banach space with separable dual. It is proved that for every ε∈ (0,1), X embeds isometrically into a Banach space W with a shrinking basis (w_n) which is (1+ ε)-monotone. Moreover, if X has further an FDD (E_n) whose strong bimonotonicity projection constant is not larger than D, then (w_n) has strong bimonotonicity projection constant not exceeding D(1 +ε). Further, if (E_n) is C-unconditional then (w_n) is C(1 + ε)-unconditional. The proof uses renorming and skipped blocking decomposition techniques. As an application, we prove that every Banach space having a shrinking D-unconditional basis with D

Related

• Asymptotic Unconditionality
• New examples of c₀-saturated Banach spaces II
• An isometrically universal Banach space with a monotone Schauder basis
• On Zippin's Embedding Theorem of Banach spaces into Banach spaces with bases
• Low distortion embeddings into Asplund Banach spaces