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

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.