Quasicomplemented Subspaces of Banach Spaces and Separable Quotients

Abstract

We present a result which generalizes the theorems of Gurariy-Kadets and Lindenstrauss-Rosenthal on quasicomplemented subspaces of Banach spaces. We also provide a solution in wide classes of Banach spaces of a problem posed by Ivan Singer concerning the existence of a w*-basic sequence in the dual of a Banach space which is biorthogonal to a given basic sequence (or more generally, a given minimal sequence) in that space, and other related problems.