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Schauder bases and the bounded approximation property in separable Banach spaces

Jorge MujicaDaniela M. Vieira — 2010

Studia Mathematica

Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties s u p n | | T | | λ + ϵ and l i m s u p n | | T | | λ . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

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