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A product of three projections

  1. 1.
    0434096 - MÚ 2015 RIV PL eng J - Článek v odborném periodiku
    Kopecká, E. - Müller, Vladimír
    A product of three projections.
    Studia mathematica. Roč. 223, č. 2 (2014), s. 175-186. ISSN 0039-3223. E-ISSN 1730-6337
    Grant CEP: GA ČR(CZ) GA14-07880S
    Institucionální podpora: RVO:67985840
    Klíčová slova: Hilbert space * projection * extension
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.610, rok: 2014
    http://journals.impan.pl/cgi-bin/doi?sm223-2-4

    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.
    Trvalý link: http://hdl.handle.net/11104/0238264

     
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