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

Abstract

In this article, we study the ccs-Daugavet, ccs-Delta, super-Daugavet, super-Delta, Daugavet, Delta, and del points in the unit balls of vector-valued function spaces C-0 (L, X), A(K, X), L-infinity (mu, X), and L-1 (mu, X). To partially or fully characterize these diametral points, we first provide improvements of several stability results under circle plus(infinity) and circle plus(1)-sums shown in the literature. For complex Banach spaces, del points are identical to Daugavet points, and so the study of del points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for L-infinity(mu) and uniform algebra when K is infinite.