Delta- and Daugavet points in Banach spaces

2020

AbstractA Δ-pointxof a Banach space is a norm-one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance 2 fromx. If, in addition, every point in the unit ball is arbitrarily close to such convex combinations,xis a Daugavet point. A Banach spaceXhas the Daugavet property if and only if every norm-one element is a Daugavet point. We show that Δ- and Daugavet points are the same inL1-spaces, inL1-preduals, as well as in a big class of Müntz spaces. We also provide an example of a Banach space where all points on the unit sphere are Δ-points, but none of them are Daugavet points. We also study the property that the unit ball is the clo…