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Structure of Rademacher subspaces in Cesàro type spaces

Volume 226 / 2015

Sergey V. Astashkin, Lech Maligranda Studia Mathematica 226 (2015), 259-279 MSC: Primary 46E30, 46B20; Secondary 46B42. DOI: 10.4064/sm226-3-4

Abstract

The structure of the closed linear span ${\mathcal R}$ of the Rademacher functions in the Cesàro space ${\rm Ces}_{\infty }$ is investigated. It is shown that every infinite-dimensional subspace of ${\mathcal R}$ either is isomorphic to $l_2$ and uncomplemented in ${\rm Ces}_{\infty }$, or contains a subspace isomorphic to $c_0$ and complemented in ${\mathcal R}$. The situation is rather different in the $p$-convexification of ${\rm Ces}_\infty $ if $1 < p <\infty $.

Authors

  • Sergey V. AstashkinDepartment of Mathematics and Mechanics
    Samara State University
    Acad. Pavlova 1
    443011 Samara, Russia
    e-mail
  • Lech MaligrandaDepartment of Engineering Sciences
    and Mathematics
    Luleå University of Technology
    SE-971 87 Luleå, Sweden
    e-mail

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