12 citations · 17 across the 5 of their papers we have counts for
8 papers
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) m…
Diameter two properties for spaces of Lipschitz functions
Rainis Haller, Andre Ostrak, Märt Põldvere
We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show…
Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open
Trond Arnold Abrahamsen, Julio Becerra Guerrero, Rainis Haller +2
We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative wea…
New applications of extremely regular function spaces
Trond A. Abrahamsen, Olav Nygaard, Märt Põldvere
Let be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of have very strong diameter properties and, for every rea…
On convex combinations of slices of the unit ball in Banach spaces
Rainis Haller, Paavo Kuuseok, Märt Põldvere
We prove that the following three properties for a Banach space are all different from each other: every finite convex combination of slices of the unit ball is (1) relatively weak…
Rough norms in spaces of operators
Rainis Haller, Johann Langemets, Märt Põldvere
We investigate sufficient and necessary conditions for the space of bounded linear operators between two Banach spaces to be rough or average rough. Our main result is that $\mathc…
Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm
Rainis Haller, Katriin Pirk, Märt Põldvere
We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has a…
On duality of diameter 2 properties
Rainis Haller, Johann Langemets, Märt Põldvere
It is known that a Banach space has the strong diameter 2 property (i.e. every convex combination of slices of the unit ball has diameter 2) if and only if the norm on its dual spa…