### Comments to Enflo's construction of 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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S. Kwapien (1972-1973)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Al-Minawi, H., Ayesh, S. (1991)

International Journal of Mathematics and Mathematical Sciences

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Giovanni Emmanuele, Kamil John (2000)

Czechoslovak Mathematical Journal

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W. Johnson, A. Szankowski (1976)

Studia Mathematica

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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 $E{\otimes}_{\epsilon}X$ 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 $F{\u2a36}_{\pi}X$. This solves in the negative a question of Taskinen....

Gerald W. Johnson, Loren V. Petersen (1977)

Commentationes Mathematicae Universitatis Carolinae

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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.

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of ${c}_{0}$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...