Set theory in infinite-dimensional vector spaces

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Abstract
We study examples of set-theoretic phenomena occurring in infinite-dimensional spaces, motivated by functional analysis. This includes equivalence relations induced by ideals of operators on a Hilbert space, a new "local" Ramsey theory for block sequences in Banach spaces and countable discrete vector spaces, analogues of selective ultrafilters and coideals in these settings, and families of infinite-dimensional subspaces which have pairwise finite-dimensional intersection. We draw analogies to the structure of the infinite subsets of the natural numbers.
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2017-08-30
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Mathematics; Banach spaces; functional analysis; mathematical logic; Ramsey theory; set theory
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Moore, Justin Tatch
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Muscalu, Florin Camil
Shore, Richard A.
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Mathematics
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Ph. D., Mathematics
Degree Level
Doctor of Philosophy
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Government Document
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Attribution 4.0 International
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dissertation or thesis
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