This article is cited in 1 paper

On the Existence of an Element with Given Deviations from an Expanding System of Subspaces

Yu. A. Skvortsov<sup>ab

a</sup> Lomonosov Moscow State University
^b Moscow Center for Fundamental and Applied Mathematics

Abstract: 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.

UDC: 517.982.256

MSC: 46B20

Received: 15.04.2023

DOI: 10.4213/mzm13982

 English version: Mathematical Notes, 2023, 114:5, 949–956

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