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 ; AIS: 0.761, rok: 2014
Web výsledku:
http://journals.impan.pl/cgi-bin/doi?sm223-2-4DOI: https://doi.org/10.4064/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