On a property of the Rademacher system and $\Lambda(2)$-spaces

S. V. Astashkin^abcd, E. M. Semenov<sup>e

a</sup> Samara National Research University, Samara, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
^d Bahcesehir University, Istanbul, Turkey
^e Voronezh State University, Voronezh, Russia

Abstract: The closed linear span of the Rademacher functions in $L^2[0,1]$ contains functions with arbitrarily large distribution, provided that the ratio of this distribution to the distribution of a standard normal variable tends to zero. A similar result is also obtained for some classes of $\Lambda(2)$-spaces.
Bibliography: 18 titles.

Keywords: Rademacher system, $L^2$-space, rearrangement invariant space, Orlicz space, independent functions, $\Lambda(2)$-space.

MSC: Primary 46B15, 46E30; Secondary 46B09

Received: 15.04.2023 and 05.12.2023

DOI: 10.4213/sm9922

 English version: Sbornik: Mathematics, 2024, 215:3, 291–307

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