On various diametral notions of points in the unit ball of some vector-valued function spaces

2024/10/07 by Han Ju Lee, Lee, Han Ju, Óscar Roldán +3
Computer Science · Mathematics · #46E40 #46J10 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Primary 46B20 #Secondary 46B04

paper · pdf · doi:10.48550/arxiv.2410.04706

openalex publication_date 2024/10/07 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28

Abstract

In this article, we study the ccs-Daugavet, ccs-Δ, super-Daugavet, super-Δ, Daugavet, Δ, and ∇ points in the unit balls of vector-valued function spaces C₀(L, X), A(K, X), L_∞(μ, X), and L₁(μ, X). To partially or fully characterize these diametral points, we first provide improvements of several stability results under ⊕_∞ and ⊕₁-sums shown in the literature. For complex Banach spaces, ∇ points are identical to Daugavet points, and so the study of ∇ points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for L_∞(μ) and uniform algebra when K is infinite.

Related

• Diametral notions for elements of the unit ball of a Banach space
• Delta- and Daugavet-points in Banach spaces
• Unconditional bases and Daugavet renormings
• Daugavet- and Delta-points in absolute sums of Banach spaces
• Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points