PFA and complemented subspaces of ℓ∞/c0

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...

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 ...

Complemented Invariant Subspaces and Interpolation Sequences

It is shown that the invariant subspace of the Bergman space Ap of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in Ap. Let D be the open unit disc of the complex plane C, and let H = H(D) denote the usual Hardy space. For 0 < p < ∞ the Bergman space A consists of analytic functions f on D such that ‖f‖p = ∫ D |f(z)| dA(z) < ∞, where dA is area mea...

On quasi-complemented subspaces of banach spaces.

Complemented Subspaces of Spaces Obtained by Interpolation

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0, A1) such that A0 and A1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, hav...