4 citations · 5 across the 11 of their papers we have counts for
12 papers · 1 filter
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 Banach space with an unconditional basis which is not slicely countably determined
Marcus Lõo, Yoël Perreau
In this note, we study the geometry of the unit ball of the Banach space generated by the adequate family of all subsets of branches of the infinite binary tree, and answer several…
The Daugavet property is equivalent to the polynomial Daugavet property
Sheldon Dantas, Miguel Martín, Yoël Perreau
In this note, we prove that the Daugavet property implies the polynomial Daugavet property, solving a longstanding open problem in the field. Our approach is based on showing that…
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…
Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and -points
Christian Cobollo, Daniel Isert, Ginés López-Pérez +6
We prove that there exists an equivalent norm on with the following properties: (1) The unit ball of $(L_\infty[0,1],\Vert\vert\cdot\ver…
A relative version of Daugavet-points and the Daugavet property
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We introduce relative versions of Daugavet-points and the Daugavet property, where the Daugavet-behavior is localized inside of some supporting slice. These points present striking…
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…
Delta-points and their implications for the geometry of Banach spaces
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We show that the Lipschitz-free space with the Radon--Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to . Furthermo…
Diametral notions for elements of the unit ball of a Banach space
Miguel Martin, Yoël Perreau, Abraham Rueda Zoca
We introduce extensions of -points and Daugavet points in which slices are replaced by relative weakly open subsets (super -points and super Daugavet points) or by convex com…
Asymptotic geometry and delta-points
Trond A. Abrahamsen, Vegard Lima, André Martiny +1
We study Daugavet- and -points in Banach spaces. A norm one element is a Daugavet-point (respectively a -point) if in every slice of the unit ball (respectively in every…
On the embeddability of countably branching bundle graphs into dual spaces
Yoël Perreau
In this note the result by A. Swift concerning the embeddability of countably branching bundle graphs into Banach spaces is extended from the context of reflexive spaces with an un…
On the embeddability of the family of countably branching trees into quasi-reflexive Banach spaces
Yoël Perreau
In this note we extend to the quasi-reflexive setting the result of F. Baudier, N. Kalton and G. Lancien concerning the non-embeddability of the family of countably branching trees…