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Properties of intersection in the geometry of sequences in Banach spaces. (English) Zbl 0604.46017

We consider properties of sequences in a Banach space through the geometrical behaviour of the closed linear spans of their subsequences. We study new families of intersection properties, generalizing the results of Courage-Davis, Plans, and Reyes. We end with a table showing the structure of a sequence by means of its intersection properties. This table, in our opinion, closes the study of ”finite” intersection properties of a sequence.

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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