The paper is based on the following construction due to Stephani from 1980. Given a collection of sequences in a Banach space X, we consider all the subsets in which every sequence has a subsequence from the given collection. This construction produces a collection of subsets of X. Conversely, given a collection of subsets of X, we consider all the sequences contained in those sets; this procedure gives us a collection of sequences in X. Thus, we have maps from collections of sequences to collections of subsets, and vice versa. We study these maps and various structures that arise as byproducts of these maps. We also investigate order properties of these maps.
Positivity – Springer Journals
Published: Oct 21, 2016
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