Subspaces and quotients of Banach spaces with shrinking unconditional bases Academic Article uri icon

abstract

  • The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient of a uniformly convex space with an unconditional finite dimensional decomposition. © 2011 Hebrew University Magnes Press.

author list (cited authors)

  • Johnson, W. B., & Zheng, B.

citation count

  • 3

complete list of authors

  • Johnson, WB||Zheng, Bentuo

publication date

  • September 2011