Subspaces and quotients of Banach spaces with shrinking unconditional bases
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.
Publication Title
Israel Journal of Mathematics
Recommended Citation
Johnson, W., & Zheng, B. (2011). Subspaces and quotients of Banach spaces with shrinking unconditional bases. Israel Journal of Mathematics, 185 (1), 375-388. https://doi.org/10.1007/s11856-011-0115-4
