Strict u-ideals in Banach spaces
Volume 195 / 2009
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.
