On spreading $c_0$-sequences in Banach spaces

Vassiliki Farmaki

Displaying similar documents to “On spreading $c_{0}$ -sequences in Banach spaces”

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Banach spaces with a supershrinking basis

Ginés López (1999)

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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 $c_{0}$ .

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Characterizations of elements of a double dual Banach space and their canonical reproductions

Vassiliki Farmaki (1993)

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For every element x** in the double dual of a separable Banach space X there exists the sequence $(x^{(2 n)})$ of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class $B_{1} (X) ╲ B_{1 / 2} (X)$ (resp. to the class $B_{1 / 4} (X)$ ) as the elements with the sequence $(x^{(2 n)})$ equivalent to the usual basis of $ℓ^{1}$ (resp. as the elements with the sequence $(x^{(4 n - 2)} - x^{(4 n)})$ equivalent to the...

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Displaying similar documents to “On spreading c 0 -sequences in Banach spaces”

Displaying similar documents to “On spreading $c_{0}$ -sequences in Banach spaces”