14 papers · 1 filter
Dual Banach spaces with the ball-covering property
Johann Langemets, Emma Mõttus, Natalia Saealle
We study ball-covering properties of dual Banach spaces and their connections with the geometry of predual unit balls. One of our main results shows that, for every separable Banac…
Transfinite Daugavet property
Antonio Avilés, Johann Langemets, Miguel Martín +1
We extend the Daugavet property and a perfect version of it to transfinite cardinals in order to distinguish between spaces with the ordinary Daugavet property by some kind of comp…
The super Alternative Daugavet property for Banach spaces
Johann Langemets, Marcus Lõo, Miguel Martín +2
We introduce the super alternative Daugavet property (super ADP) which lies strictly between the Daugavet property and the Alternative Daugavet property as follows. A Banach space…
Slicely countably determined points in Banach spaces
Johann Langemets, Marcus Lõo, Miguel Martin +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 points…
Unconditional bases and Daugavet renormings
Rainis Haller, Johann Langemets, Yoël Perreau +1
We introduce a new diametral notion for points of the unit sphere of Banach spaces, that naturally complements the notion of Delta-points, but is weaker than the notion of Daugavet…
Transfinite almost square Banach spaces
Antonio Avilés, Stefano Ciaci, Johann Langemets +2
It is known that a Banach space contains an isomorphic copy of if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versio…