On the linear polarization constants of finite dimensional spaces

2017/03/18 by Daniel Carando, Carando, Daniel, Damián Pinasco +3
Mathematics · #46B20 #51M16 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B20 #msc:51M16

paper · pdf · doi:10.48550/arxiv.1703.06316

20 pages

arxiv created 2017/03/18 · openalex publication_date 2017/03/18 · arxiv updated 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces ℓ_p^d: they behave as √[p]d if 1≤ p≤ 2 and as √(d) if 2≤ p<∞. For p=∞ we get the asymptotic behavior up to a logarithmic factor

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