About: The Hundal example revisited

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Článek zjednodušuje a zesiluje Hundalův příklad, že iterací projekce na dvě konvexní množiny v Hilbertově prostoru nemusí konvergovat v normě, ačkoliv konverguje v slabé topologii. (cs) Hundal has recently solved a long-standing open problem by constructing an ingenious example of a cone and a half-space in the Hilbert space ${/ell_2}$, which intersect at the origin, such that the corresponding sequence of alternating nearest point mappings (although weakly convergent) does not converge in norm to zero. Using geometric insight, we modify this example and simplify its verification. In our modified example, the cone and the half-space may be disjoint. Hundal has recently solved a long-standing open problem by constructing an ingenious example of a cone and a half-space in the Hilbert space ${/ell_2}$, which intersect at the origin, such that the corresponding sequence of alternating nearest point mappings (although weakly convergent) does not converge in norm to zero. Using geometric insight, we modify this example and simplify its verification. In our modified example, the cone and the half-space may be disjoint. (en)
Title	Hundalův příklad ještě jednou (cs) The Hundal example revisited The Hundal example revisited (en)
skos:prefLabel	Hundalův příklad ještě jednou (cs) The Hundal example revisited The Hundal example revisited (en)
skos:notation	RIV/67985840:_____/03:00106845!RIV/2005/AV0/A05005/N
http://linked.open.../vavai/riv/strany	411;427
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1019103), Z(AV0Z1019905)
http://linked.open...iv/cisloPeriodika	-
http://linked.open...vai/riv/dodaniDat	2005
http://linked.open...aciTvurceVysledku	Kopecká, Eva
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	609463
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/03:00106845
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	long-standing open problem;Hilbert space (en)
http://linked.open.../riv/klicoveSlovo	Hilbert space long-standing open problem
http://linked.open...odStatuVydavatele	JP - Japonsko
http://linked.open...ontrolniKodProRIV	[98B6B28AE83E]
http://linked.open...i/riv/nazevZdroje	Journal of Nonlinear and Convex Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Lipschitz mapping and null sets
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	4
http://linked.open...iv/tvurceVysledku	Reich, S. Matoušková, Eva
http://linked.open...n/vavai/riv/zamer	Complex development of all branches of mathematics with regard to the needs of physics and technology
issn	1345-4773
number of pages	17 (xsd:int)

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