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Schauder bases and the bounded approximation property in separable Banach spaces

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Mujica J., Vieira D.

Studia Mathematica

2010

tom 196

nr 1

1-12

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 $sup_{n∈ ℕ } ||Tₙ|| ≤ λ + ϵ$ and $limsup_{n→ ∞} ||Tₙ|| ≤ λ$. This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

Ograniczanie wyników

1 Studia Mathematica

1 Mujica J.

1 Vieira D.

1 2010

Wyniki wyszukiwania

Schauder bases and the bounded approximation property in separable Banach spaces