Banach spaces whose duals contain complemented subspaces isomorphic to C[0, 1]

ON BANACH SPACES WHOSE DUALS ARE ISOMORPHIC TO l1(Γ)

In this paper we present new characterizations of Banach spaces whose duals are isomorphic to l1(Γ), extending results of Stegall, Lewis-Stegall and Cilia-D’Anna-Gutiérrez.

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...

Isomorphic and isometric copies of l∞(Γ) in duals of Banach spaces and Banach lattices

Let X and E be a Banach space and a real Banach lattice, respectively, and let Γ denote an infinite set. We give concise proofs of the following results: (1) The dual space X contains an isometric copy of c0 iff X contains an isometric copy of l∞, and (2) E contains a lattice-isometric copy of c0(Γ) iff E contains a lattice-isometric copy of l∞(Γ).

On c0-saturated Banach spaces

A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. A c0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l2 is constructed. A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. In [2] and [3], it was asked whether all quotient spaces ...