Počet záznamů: 1
A product of three projections
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SYSNO ASEP 0434096 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A product of three projections Tvůrce(i) Kopecká, E. (AT)
Müller, Vladimír (MU-W) RID, SAI, ORCIDZdroj.dok. Studia mathematica. - : Polska Akademia Nauk - ISSN 0039-3223
Roč. 223, č. 2 (2014), s. 175-186Poč.str. 12 s. Jazyk dok. eng - angličtina Země vyd. PL - Polsko Klíč. slova Hilbert space ; projection ; extension Vědní obor RIV BA - Obecná matematika CEP GA14-07880S GA ČR - Grantová agentura ČR Institucionální podpora MU-W - RVO:67985840 UT WOS 000348884900004 EID SCOPUS 84908307853 DOI https://doi.org/10.4064/sm223-2-4 Anotace Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam Paszkiewicz constructed five subspaces of an infinite-dimensional Hilbert space and a sequence of projections on them which does not converge in norm. We construct three such subspaces, resolving the problem fully. As a corollary we observe that the Lipschitz constant of a certain Whitney-type extension does in general depend on the dimension of the underlying space. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2015
Počet záznamů: 1