We introduce extensions of $\Delta $-points and Daugavet points in which slices are
replaced by relative weakly open subsets (super $\Delta $-points and super Daugavet …

We extend the (attaining of) strong diameter two property to infinite cardinals. In particular, a
Banach space has the 1-norming attaining strong diameter two property with respect to ω (1 …

We introduce slicely countably determined points (SCD points) of a bounded and convex
subset of a Banach space which extends the notions of denting points, strongly regular …

We characterise the class of those Banach spaces in which every convex combination of
slices of the unit ball intersects the unit sphere as the class of those spaces in which every …

We study versions of the diameter two properties where the diameter of slices, weakly
relatively open subsets, or convex combinations of slices of the unit ball is attained. We also …

We introduce and study Banach spaces which have property CWO, ie, every finite convex
combination of relatively weakly open subsets of their unit ball is open in the relative weak …

We introduce extensions of Δ-points and Daugavet points in which slices are replaced by
relatively weakly open subsets (super Δ-points and super Daugavet points) or by convex …

We prove that given a locally compact Hausdorff space K and a compact C^*∗-algebra AA,
the C^*∗-algebra C (K, A) C (K, A) satisfies (P1)(P1), namely that every convex combination …

We study Banach spaces with a weak stable unit ball, that is, Banach spaces where every
convex combination of relatively weakly open subsets in its unit ball is again a relatively …