Do projections stay close together?

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F09%3A00321374" target="_blank" >RIV/67985840:_____/09:00321374 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Do projections stay close together?
Original language description
We estimate the rate of convergence of products of projections on K intersecting lines in the Hilbert space. More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in Hilbert space. Assume that thesum of the squares of the distances of the consecutive iterates is less than epsilon. We show that if epsilon tends to zero, then the diameter of the orbit tends to zero uniformly for all families of a fixed number K of lines. We relate this result to questions concerning convergence of products of projections on finite families of closed subspaces of the Hilbert space.
Czech name
Zůstávají projekce pohromadě?
Czech description
Článek se zabývá rychlostí konvergence iterací projekcí na K přímek v Hilbertově prostoru. Výsledek je dán do souvislosti s otázkou konvergence iterací projekci na K podprostoru Hilbertova prostoru.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F06%2F0018" target="_blank" >GA201/06/0018: Topological structures in functional analysis</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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