Structure of Rademacher subspaces in Cesàro type spaces
Volume 226 / 2015
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 $.
