On the equality of injective and projective tensor products
Hans Jarchow, Kamil John (1988)
Czechoslovak Mathematical Journal
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Hans Jarchow, Kamil John (1988)
Czechoslovak Mathematical Journal
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J. C. Díaz, J. A. López Molina, M. J. Rivera (1990)
Collectanea Mathematica
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N. J. Nielsen (1980-1981)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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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....
S. Kwapien (1972-1973)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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 , 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). ...
Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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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.
Cho, Chong-Man (1992)
International Journal of Mathematics and Mathematical Sciences
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Bertram Yood (2008)
Studia Mathematica
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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.
David E. Edmunds, Jan Lang (2013)
Studia Mathematica
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We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.