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
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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?
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
Affiliations des auteurs :
Aleksei Lissitsin 1
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title = {A unified approach to the strong approximation property and the weak bounded
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journal = {Studia Mathematica},
pages = {199--214},
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volume = {211},
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year = {2012},
doi = {10.4064/sm211-3-2},
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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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