A+ CATEGORY SCIENTIFIC UNIT

Strict u-ideals in Banach spaces

Volume 195 / 2009

Vegard Lima, Åsvald Lima Studia Mathematica 195 (2009), 275-285 MSC: Primary 46B04, 46B20. DOI: 10.4064/sm195-3-6

Abstract

We study strict u-ideals in Banach spaces. A Banach space $X$ is a strict u-ideal in its bidual when the canonical decomposition $X^{***} = X^* \oplus X^\perp $ is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if $X$ is a strict u-ideal in a Banach space $Y$ then $X$ contains $c_0$. We also show that $\ell _\infty $ is not a u-ideal.

Authors

  • Vegard LimaAalesund University College
    Service Box 17
    N-6025 Ålesund, Norway
    e-mail
  • Åsvald LimaDepartment of Mathematics
    University of Agder
    Serviceboks 422
    4604 Kristiansand, Norway
    e-mail

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