An example concerning reflexivity

R. Herman; R. Whitley

Displaying similar documents to “An example concerning reflexivity”

On w-sequential convergence, type P bases, and reflexivity

R. Fleming, R. McWilliams, J. Retherford (1965)

Studia Mathematica

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On Banach spaces in which every M-basis is a generalized summation basis

Ivan Singer (1979)

Banach Center Publications

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On finite dimensional subspaces of Banach spaces with local unconditional structure

William Johnson (1974)

Studia Mathematica

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Basic sequences and reflexivity of Banach spaces

I. Singer (1962)

Studia Mathematica

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Banach spaces with a supershrinking basis

Ginés López (1999)

Studia Mathematica

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We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without $c_{0}$ copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the $c_{0}$ -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in $c_{0}$ .

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.