Geodesic
Weak Limits of Consecutive Projections and of Greedy Steps
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 64-72

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Let $H$ be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto $K\geq 2$ closed convex sets in $H$ and the parallel properties of weak limit points of the residuals of random greedy approximation with respect to $K$ dictionaries. In the case of convex sets these properties imply weak convergence in all the cases known so far. In particular, we give a short proof of the theorem of Amemiya and Ando on weak convergence when the convex sets are subspaces. The question of weak convergence in general remains open.
Keywords: projections, greedy approximations, convex set, dictionary, Hilbert space. 
@article{TRSPY_2022_319_a4,
     author = {Petr A. Borodin and Eva Kopeck\'a},
     title = {Weak {Limits} of {Consecutive} {Projections} and of {Greedy} {Steps}},
     journal = {Informatics and Automation},
     pages = {64--72},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a4/}
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Petr A. Borodin; Eva Kopecká. Weak Limits of Consecutive Projections and of Greedy Steps. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 64-72. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a4/