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

Author:

Astashkin Sergei Vladimirovich1234,Semenov Evgenii Mikhailovich5

Affiliation:

1. Bahcesehir University, Istanbul, Turkey

2. Lomonosov Moscow State University, Moscow, Russia

3. Samara National Research University, Samara, Russia

4. Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

5. 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.

Funder

Russian Foundation for Basic Research

Ministry of Science and Higher Education of the Russian Federation

Publisher

Steklov Mathematical Institute

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