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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A local Ramsey theory for block sequences


Author: Iian B. Smythe
Journal: Trans. Amer. Math. Soc. 370 (2018), 8859-8893
MSC (2010): Primary 05D10, 03E05; Secondary 46B20
DOI: https://doi.org/10.1090/tran/7448
Published electronically: August 15, 2018
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Abstract: We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias's selective coideal form of Silver's theorem for analytic partitions of $ [\mathbb{N}]^\infty $. Under large cardinals, these results are extended to partitions in $ \mathbf {L}(\mathbb{R}),$ and $ \mathbf {L}(\mathbb{R})$-generic filters of block sequences are characterized. Variants of these results are also established for block sequences in Banach spaces and for projections in the Calkin algebra.


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Additional Information

Iian B. Smythe
Affiliation: Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854
Email: i.smythe@rutgers.edu

DOI: https://doi.org/10.1090/tran/7448
Received by editor(s): September 28, 2016
Received by editor(s) in revised form: October 20, 2017
Published electronically: August 15, 2018
Additional Notes: The author is partially supported by NSERC award PGSD2-453779-2014 and NSF grant DMS-1600635.
Article copyright: © Copyright 2018 American Mathematical Society

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