39 citations · 56 across the 8 of their papers we have counts for
13 papers · 1 filter
Strictly convex renormings and the diameter 2 property
Olav Nygaard, Märt Põldvere, Stanimir Troyansky +1
A Banach space (or its norm) is said to have the diameter property (DP in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter . We…
Isometric factorization of vector measures and applications to spaces of integrable functions
Olav Nygaard, José Rodríguez
Let be a Banach space, be a -algebra, and be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski fact…
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…
Strongly extreme points and approximation properties
Trond A. Abrahamsen, Petr Hájek, Olav Nygaard +1
We show that if is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approxi…
Two properties of Müntz spaces
Trond A. Abrahamsen, Aleksander Leraand, André Martiny +1
We show that Müntz spaces, as subspaces of , contain asymptotically isometric copies of and that their dual spaces are octahedral.
Diameter two properties, convexity and smoothness
Trond A. Abrahamsen, Vegard Lima, Olav Nygaard +1
We study smoothness and strict convexity of (the bidual) of Banach spaces in the presence of diameter 2 properties. We prove that the strong diameter 2 property prevents the bidual…