5 papers
Weak stability and binary convex combinations of slices
Rainis Haller
We study weak openness and related geometric properties of convex combinations of slices of the unit balls of Banach spaces. We prove that, for every , properties $\mathrm…
Plasticity of the unit ball of the real Banach space
Rainis Haller, Nikita Leo
We prove that the closed unit ball of the real Banach space is plastic, that is, every non-expansive bijection from the unit ball onto itself is an isometry. The main…
A counterexample for the Daugavet index of thickness in -sums
Rainis Haller, Andre Ostrak
We give a negative answer to a question of Haller-Langemets-Lima-Nadel-Rueda Zoca asking whether, for all Banach spaces and , the Daugavet index of thickness satisfies \[ T(…
Norm-one points in convex combinations of relatively weakly open subsets of the unit ball in the spaces
Rainis Haller, Paavo Kuuseok, Märt Põldvere
In a paper published in 2020 in Studia Mathematica, Abrahamsen et al. proved that in the real space , where is a non-zero -finite (countably additive non-negative…
The local diameter two property and the diameter two property in spaces of Lipschitz functions
Rainis Haller, Jaan Kristjan Kaasik, Andre Ostrak
We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the $w…