Bounded approximation properties in terms of C[0, 1]

• Autores: Asvald Lima, Vegard Lima, Eve Oja
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 1, 2012, págs. 45-58
• Idioma: inglés
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• Resumen

  • Let X be a Banach space and let I be the Banach operator ideal of integral operators. We prove that X has the λ-bounded approximation property (λ-BAP) if and only if for every operator T∈I(X,C[0,1]∗) there exists a net (Sα) of finite-rank operators on X such that Sα→IX pointwise and 26767 \limsup_\alpha\|TS_\alpha\|_{\mathcal I}\leq\lambda\|T\|_{\mathcal I}. 26767 We also prove that replacing I by the ideal N of nuclear operators yields a condition which is equivalent to the weak λ-BAP.