Displaying similar documents to “Weak compactness criteria and convergences in LE1(μ).”

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...

Representing and absolutely representing systems

V. Kadets, Yu. Korobeĭnik (1992)

Studia Mathematica

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We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.