7 papers
A strictly convex and smooth Banach space with the Daugavet property
Sheldon Dantas, Jaan Kristjan Kaasik, Yoël Perreau
We construct equivalent norms on , arbitrarily close to the usual -norm, which are weakly midpoint locally uniformly rotund and Gâteaux smooth, and whose dual norms…
A note on attaining diameter two properties in Lipschitz-free spaces
Jaan Kristjan Kaasik
We prove that in Lipschitz-free spaces the strong diameter two property, the diameter two property, and the local diameter two property coincide with their corresponding attaining…
Universality of Lipschitz quotients and the curve-flat index
Jaan Kristjan Kaasik, Andrés Quilis
We study universality of Lipschitz quotients. First, we modify a construction of Johnson, Lindenstrauss, Preiss and Schechtman to obtain a complete separable metric space that has…
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…
Separating diameter two properties from their weak-star counterparts in spaces of Lipschitz functions
Rainis Haller, Jaan Kristjan Kaasik, Andre Ostrak
We address some open problems concerning Banach spaces of real-valued Lipschitz functions. Specifically, we prove that the diameter two properties differ from their weak-star count…
Weakly almost square Lipschitz-free spaces
Jaan Kristjan Kaasik, Triinu Veeorg
We construct a Lipschitz-free space that is locally almost square but not weakly almost square; this is the first example of such a Banach space. We also prove a result, which indi…