Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Haller, Rainis"'
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 counterparts in these spaces. In particular, we establish the existence of
Externí odkaz:
http://arxiv.org/abs/2404.11430
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 points. We prove that this notion can be used to provide a new geomet
Externí odkaz:
http://arxiv.org/abs/2303.07037
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 that: the diameter two property, the strong diameter two property, and
Externí odkaz:
http://arxiv.org/abs/2205.13287
We prove that the Lipschitz-free space over a metric space M is locally almost square whenever M is a length space. Consequently, the Lipschitz-free space is locally almost square if and only if it has the Daugavet property. We also show that a Lipsc
Externí odkaz:
http://arxiv.org/abs/2205.02685
Publikováno v:
In Journal of Functional Analysis 1 October 2024 287(7)
We prove that Banach spaces $\ell_1\oplus_2\mathbb{R}$ and $X\oplus_\infty Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).
Externí odkaz:
http://arxiv.org/abs/2111.10122
Publikováno v:
In Journal of Functional Analysis 15 June 2024 286(12)
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index
Externí odkaz:
http://arxiv.org/abs/2005.02045
A Daugavet-point (resp.~$\Delta$-point) of a Banach space is a norm one element $x$ for which every point in the unit ball (resp.~element $x$ itself) is in the closed convex hull of unit ball elements that are almost at distance 2 from $x$. A Banach
Externí odkaz:
http://arxiv.org/abs/2001.06197
A $\Delta$-point $x$ of a Banach space is a norm one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance $2$ from $x$. If, in addition, every point in the unit ball is arbitrarily close to
Externí odkaz:
http://arxiv.org/abs/1812.02450