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Session 36. Topology in Functional Analysis
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Unconditional bases in Banach spaces and Tukey ordering |
Grzegorz Plebanek, Uniwersytet Wrocławski, Poland
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The talk is based on the joint work with Antonio Avilés and José Rodrígez
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Let \(B=(e_n)_n\) be an unconditional basic sequence in a Banach space \(X\) and let \(\mathcal{N}(B)\) be a family
of those sets \(A\subseteq{\mathbb N}\) for which \((e_n)_{n\in A}\) is a weakly null subsequence.
One can examine properties of \(B=(e_n)_n\) by looking at the cofinal structure of the ideal \(\mathcal{N}(B)\).
We present a certain classification of bases in Banach spaces using Tukey reductions between partially ordered sets of the form \(\mathcal{N}(B)\).
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