Schauder bases and the bounded approximation property in separable Banach spaces

• Autorzy: Jorge Mujica , Daniela M. Vieira
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 46B15: Summability and bases
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 1
• Strony: 1-12

Daty

wydano

2010

Twórcy

autor

Jorge Mujica

• IMECC-UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil

autor

Daniela M. Vieira

• IMECC-UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
• Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, SP, Brazil

Identyfikatory

DOI

10.4064/sm196-1-1