Geodesic
A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces
Aleksei Lissitsin1
1Faculty of Mathematics and Computer Science Tartu University J. Liivi 2 EE-50409 Tartu, Estonia
Studia Mathematica, Tome 211 (2012) no. 3, pp. 199-214
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider convex versions of the strong approximation property and the weak bounded approximation property and develop a unified approach to their treatment introducing the inner and outer $\varLambda$-bounded approximation properties for a pair consisting of an operator ideal and a space ideal. We characterize this type of properties in a general setting and, using the isometric DFJP-factorization of operator ideals, provide a range of examples for this characterization, eventually answering a question due to Lima, Lima, and Oja: Are there larger Banach operator ideals than $\mathcal W$ yielding the weak bounded approximation property?
DOI : 10.4064/sm211-3-2
Keywords: consider convex versions strong approximation property weak bounded approximation property develop unified approach their treatment introducing inner outer varlambda bounded approximation properties pair consisting operator ideal space ideal characterize type properties general setting using isometric dfjp factorization operator ideals provide range examples characterization eventually answering question due lima lima oja there larger banach operator ideals mathcal yielding weak bounded approximation property

Aleksei Lissitsin  1

1 Faculty of Mathematics and Computer Science Tartu University J. Liivi 2 EE-50409 Tartu, Estonia 
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Aleksei Lissitsin. A unified approach to the strong approximation property and the weak bounded
approximation property
 of Banach spaces. Studia Mathematica, Tome 211 (2012) no. 3, pp. 199-214. doi: 10.4064/sm211-3-2

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