Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Langemets, Johann"'
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 and much more. We completely characterize SCD points in the unit balls
Externí odkaz:
http://arxiv.org/abs/2311.03064
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
It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate them to t
Externí odkaz:
http://arxiv.org/abs/2204.13449
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 September 2024 537(1)
We extend the (attaining of) strong diameter two property to infinite cardinals. In particular, a Banach space has the 1-norming attaining strong diameter two property with respect to $\omega$ (1-ASD2P$_\omega$ for short) if every convex series of sl
Externí odkaz:
http://arxiv.org/abs/2109.15001
Publikováno v:
In Journal of Functional Analysis 15 June 2024 286(12)
In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of $\ell_1$ if and only if it can be equivalently renormed to be octahedral. It is known that octahedral norms can be characterized by means of covering the unit sphere by a
Externí odkaz:
http://arxiv.org/abs/2102.13525
Autor:
Langemets, Johann, Pirk, Katriin
We prove that the diametral diameter two properties are inherited by $F$-ideals (e.g., $M$-ideals). On the other hand, these properties are lifted from an $M$-ideal to the superspace under strong geometric assumptions. We also show that all of the di
Externí odkaz:
http://arxiv.org/abs/2012.09492
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
Autor:
Langemets, Johann
We continue the investigation of the behaviour of diameter two properties in tensor products of Banach spaces. Our main result shows that the symmetric strong diameter two property is stable by taking projective tensor products. We also prove a resul
Externí odkaz:
http://arxiv.org/abs/2003.09686