Do projections stay close together?

0321374 - MÚ 2009 RIV US eng J - Journal Article
Kirchheim, B. - Kopecká, Eva - Müller, S.
Do projections stay close together?
[Zůstávají projekce pohromadě?]
Journal of Mathematical Analysis and Applications. Roč. 350, č. 2 (2009), s. 859-871. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA201/06/0018
Institutional research plan: CEZ:AV0Z10190503
Keywords : projection * iteration * Hilbert space
Subject RIV: BA - General Mathematics
Impact factor: 1.225, year: 2009

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 the sum 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.

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.
Permanent Link: http://hdl.handle.net/11104/0169942