Enflo's example of a Banach space without the approximation property
S. Kwapien (1972-1973)
Séminaire Équations aux dérivées partielles (Polytechnique)
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S. Kwapien (1972-1973)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Eve Oja (2010)
Banach Center Publications
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This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?
Kamal, Aref (1998)
International Journal of Mathematics and Mathematical Sciences
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T. D. Narang (1985)
Matematički Vesnik
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Alfredo Peris (1993)
Studia Mathematica
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We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for . This solves in the negative a question of Taskinen....
W. Johnson, A. Szankowski (1976)
Studia Mathematica
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Juan Carlos Cabello Piñar (1990)
Collectanea Mathematica
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The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.
Eve Oja (2006)
RACSAM
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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;...
Al-Minawi, H., Ayesh, S. (1991)
International Journal of Mathematics and Mathematical Sciences
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Elmer Bonder (1985)
Mathematica Scandinavica
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Przemyslaw Wojtaszczyk (1972)
Mémoires de la Société Mathématique de France
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