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pro vyhledávání: '"Pirk, Katriin"'
We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banac
Externí odkaz:
http://arxiv.org/abs/2409.04292
On generic convergence of successive approximations of mappings with convex and compact point images
We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping
Externí odkaz:
http://arxiv.org/abs/2211.02298
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
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
We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under 1-sums, i.e., the direct s
Externí odkaz:
http://arxiv.org/abs/1603.08082
Publikováno v:
Monatshefte für Mathematik; Dec2023, Vol. 202 Issue 4, p659-683, 25p
Autor:
Pirk, Katriin
Banachi ruumidel vaadeldavate geomeetriliste omaduste seas on äärmuslik ja hästi uuritud Daugaveti omadus. Sellise omadusega Banachi ruumi veidruseks on, et ühikkera iga viilu diameeter on 2 ehk tal on diameeter-2 omadus. Näiteks c_0, l_∞, C[0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______1018::0f7025206bf93e865aa8fe36d08f3eee
http://hdl.handle.net/10062/68458
http://hdl.handle.net/10062/68458
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