On complemented subspaces and unconditional bases in $l_{p}+l_{q}$

On Contractively Complemented Subspaces

Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...

Block bases of the Haar system as complemented subspaces of . . .

It is shown that the span of fa i h i b i e i g n i=1 , where fh i g is the Haar system in L p and fe i g the canonical basis of`p , is well isomorphic to a well complemented subspace of L p ; 2 < p < 1. As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in L p ; 2 < p < 1, any block basis of which is well isomorphic to a well complemented subspac...

Subspaces and Quotients of Banach Spaces with Shrinking Unconditional Bases

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 an unconditional basis iff it is isomorphic to a quotient of a space with an unconditional basis, which solves...

On quasi-complemented subspaces of banach spaces.

PFA and complemented subspaces of ℓ∞/c0

The Banach space `∞/c0 is isomorphic to the linear space of continuous functions on N∗ with the supremum norm, C(N∗). Similarly, the canonical representation of the `∞ sum of `∞/c0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N∗. It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of...