The problem and degrees of non-reflexivity
W. Davis, W. Johnson, J. Lindenstrauss (1976)
Studia Mathematica
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Displaying similar documents to “On the principle of local reflexivity”
The problem and degrees of non-reflexivity
What is "local theory of Banach spaces"?
Albrecht Pietsch (1999)
Studia Mathematica
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Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.
Local dual spaces of a Banach space
Manuel González, Antonio Martínez-Abejón (2001)
Studia Mathematica
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We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing...
The main triangle projection in matrix spaces and its applications
S. Kwapień, A. Pełczyński (1970)
Studia Mathematica
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On isomorphisms between certain subalgebras of B(X)
H. Brown, F. Cass, I. Robinson (1978)
Studia Mathematica
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Isometries in , generating functions and extremal problems
Vlastimil Pták (1985)
Časopis pro pěstování matematiky
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Some results on Banach spaces without local unconditional structure
Gilles Pisier (1978)
Compositio Mathematica
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Extension of operators from weak*-closed sub-spaces of into C(K) spaces
W. Johnson, M. Zippin (1995)
Studia Mathematica
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It is proved that every operator from a weak*-closed subspace of into a space C(K) of continuous functions on a compact Hausdorff space K can be extended to an operator from to C(K).
Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Steven Bellenot (1978)
Studia Mathematica
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On prequojections and their duals.
M. I. Ostrovskii (1998)
Revista Matemática Complutense
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The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce...