A product of three projections

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00434096" target="_blank" >RIV/67985840:_____/14:00434096 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/sm223-2-4" target="_blank" >http://dx.doi.org/10.4064/sm223-2-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm223-2-4" target="_blank" >10.4064/sm223-2-4</a>

Result language
angličtina
Original language name
A product of three projections
Original language description
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 subspacesof 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.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA14-07880S" target="_blank" >GA14-07880S: Methods of function theory and Banach algebras in operator theory V.</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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