In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of ℓ1 if and
only if it can be equivalently renormed to be octahedral. It is known that octahedral norms …

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 …

A result of G. Godefroy asserts that a Banach space X contains an isomorphic copy of ℓ 1 if
and only if there is an equivalent norm|||·||| such that, for every finite-dimensional subspace Y …

We study a local version of the ball-covering problem in Banach spaces, and obtain a
complete solution to it in terms of the norm derivatives. We illustrate the advantage of the …

A result of G. Godefroy asserts that a Banach space X contains an isomorphic copy of ℓ 1 if
and only if there is an equivalent norm|||⋅||| such that, for every finite-dimensional subspace …