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Displaying similar documents to “The characteristic of weak convergence on Banach sequence lattices.”

Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz (1997)

Collectanea Mathematica

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A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.

On spreading c 0 -sequences in Banach spaces

Vassiliki Farmaki (1999)

Studia Mathematica

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We introduce and study the spreading-(s) and the spreading-(u) property of a Banach space and their relations. A space has the spreading-(s) property if every normalized weakly null sequence has a subsequence with a spreading model equivalent to the usual basis of c 0 ; while it has the spreading-(u) property if every weak Cauchy and non-weakly convergent sequence has a convex block subsequence with a spreading model equivalent to the summing basis of c 0 . The main results proved are the...

A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

G. Androulakis (1998)

Studia Mathematica

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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...