The impact of the Radon-Nikodym property on the weak bounded approximation property.

Título inglés	The impact of the Radon-Nikodym property on the weak bounded approximation property.
Título español	El impacto de la propiedad de Radon-Nikodym en la propiedad de aproximación acotada débil.
Autor/es	Oja, Eve
Organización	Fac. Math. Comput. Sci. Tartu Univ., Tartu, Estonia
Revista	1578-7303
Publicación	2006, 100 (1-2): 325-331, 18 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	A Banach space X is said to have the weak λ-bounded approximation property if for every separable reflexive Banach space Y and for every compact operator T : X → Y, there exists a net (Sα) of finite-rank operators on X such that supα ||TSα|| ≤ λ||T|| and Sα → IX uniformly on compact subsets of X. We prove the following theorem. Let X** or Y* have the Radon-Nikodym property; if X has the weak λ-bounded approximation property, then for every bounded linear operator T: X → Y, there exists a net (Sα) as in the above definition. It follows that the weak λ-bounded and λ-bounded approximation properties are equivalent for X whenever X* or X** has the Radon-Nikodym property. Relying on Johnson?s theorem on lifting of the metric approximation property from Banach spaces to their dual spaces, this yields a new proof of the classical result: if X* has the approximation property and X* or X** has the Radon-Nikodym property, then X* has the metric approximation property.
Código MathReviews	MR2267414
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