2015/03/20 by Asuman Güven Aksoy, Aksoy, Asuman Guven, Grzegorz Lewicki +1
Computer Science · Mathematics · #41A35 #41A65 #47A12 #47H10 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1503.06194
openalex publication_date 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we survey some recent results concerning the numerical index n(⋅) for large classes of Banach spaces, including vector valued ℓp-spaces and ℓp-sums of Banach spaces where 1≤ p < ∞. In particular by defining two conditions on a norm of a Banach space X, namely a Local Characterization Condition (LCC) and a Global Characterization Condition (GCC), we are able to show that if a norm on X satisfies the (LCC), then n(X) = limm n(Xm). For the case in which ℕ is replaced by a directed, infinite set S, we will prove an analogous result for X satisfying the (GCC). Our approach is motivated by the fact that n(Lp(μ, X))= n(ℓp(X)) = limm n(ℓpm (X)) \cite aga-ed-kham.