Displaying similar documents to “ L 1 spaces fail a certain approximative property.”

Topological tensor products of a Fréchet-Schwartz space and a Banach space

Alfredo Peris (1993)

Studia Mathematica

Similarity:

We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that E ε 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 π X . This solves in the negative a question of Taskinen....

Containing l or c and best approximation.

Juan Carlos Cabello Piñar (1990)

Collectanea Mathematica

Similarity:

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.

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

Similarity:

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). ...