Limit Theorems for Numerical Index

2011/06/23 by Asuman Güven Aksoy, Aksoy, Asuman Güven, Grzegorz Lewicki +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1106.4822

openalex publication_date 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We improve upon on a limit theorem for numerical index for large classes of Banach spaces including vector valued ℓ_p-spaces and ℓ_p-sums of Banach spaces where 1≤ p ≤ ∞. We first prove n₁(X) = lim_m n₁(X_m) for a modified numerical index n₁( . ). Later, we establish if a norm on X satisfies the local characterization condition, then n(X) = lim_m n(X_m). We also present an example of a Banach space where the local characterization condition is satisfied.

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