The universality of ℓ1 as a dual space Academic Article uri icon

abstract

  • Let X be a Banach space with a separable dual. We prove that X embeds isomorphically into a L ∞ space Z whose dual is isomorphic to ℓ1. If, moreover, U is a space with separable dual, so that U and X are totally incomparable, then we construct such a Z, so that Z and U are totally incomparable. If X is separable and reflexive, we show that Z can be made to be somewhat reflexive. © 2010 Springer-Verlag.

author list (cited authors)

  • Freeman, D., Odell, E., & Schlumprecht, T. h.

citation count

  • 15

publication date

  • November 2010