Twisted properties of banach spaces

  • Jesús M. F. Castillo
  • Manuel Gonzáles
  • Anatolij M. Plichko
  • David Yost

Abstract

If $\mathcal P$, $\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\mathcal P$-by-$\mathcal Q$ (or is a $\mathcal P$-by-$\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\mathcal P$ such that the corresponding quotient $X/Y$ has property $\mathcal Q$. The choices $\mathcal P,\mathcal Q \in\{\hbox{separable, reflexive}\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For example, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new example of a Banach space property which is not a 3-space property but whose dual is a 3-space property.
Published
2001-12-01
How to Cite
Castillo, J. M. F., Gonzáles, M., Plichko, A. M., & Yost, D. (2001). Twisted properties of banach spaces. MATHEMATICA SCANDINAVICA, 89(2), 217-244. https://doi.org/10.7146/math.scand.a-14339
Section
Articles