Geodesic
On the Existence of an Element with Given Deviations from an Expanding System of Subspaces
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 780-788

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We expand the class of deviation sequences for which the problem on the existence of an element of a Banach space with these deviations from a system of nested subspaces is solved positively regardless of the space and the system of subspaces. This result is used to narrow the gap between the weak asymptotics constants in S. V. Konyagin's theorem on the existence of an element whose deviations are asymptotically close to given ones.
Keywords: Banach space, subspace, deviations, Bernstein problem. 
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     author = {Yu. A. Skvortsov},
     title = {On the {Existence} of an {Element} with {Given} {Deviations} from an {Expanding} {System} of {Subspaces}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a10/}
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Yu. A. Skvortsov. On the Existence of an Element with Given Deviations from an Expanding System of Subspaces. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 780-788. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a10/