A+ CATEGORY SCIENTIFIC UNIT

Subspaces of $\ell _2(X)$ and ${\rm Rad}(X)$ without local unconditional structure

Volume 149 / 2002

Ryszard A. Komorowski, Nicole Tomczak-Jaegermann Studia Mathematica 149 (2002), 1-21 MSC: 46B03, 46B07. DOI: 10.4064/sm149-1-1

Abstract

It is shown that if a Banach space $X$ is not isomorphic to a Hilbert space then the spaces $\ell _2(X)$ and $\mathop {\rm Rad}\nolimits (X)$ contain a subspace $Z$ without local unconditional structure, and therefore without an unconditional basis. Moreover, if $X$ is of cotype $r <\infty $, then a subspace $Z$ of $\ell _2(X)$ can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.

Authors

  • Ryszard A. KomorowskiInstitute of Mathematics
    Wrocław Technical University
    50-370 Wrocław, Poland
    e-mail
  • Nicole Tomczak-JaegermannDepartment of Mathematical Sciences
    University of Alberta
    Edmonton, Alberta
    Canada T6G 2G1
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image