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Bases of random unconditional convergence in Banach spaces


Authors: J. Lopez-Abad and P. Tradacete
Journal: Trans. Amer. Math. Soc. 368 (2016), 9001-9032
MSC (2010): Primary 46B09, 46B15
DOI: https://doi.org/10.1090/tran/6636
Published electronically: March 18, 2016
MathSciNet review: 3551596
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Abstract: We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases and existence of unconditional subsequences.


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J. Lopez-Abad
Affiliation: Instituto de Ciencias Matemáticas (ICMAT), CSIC-UAM-UC3M-UCM, C/Nicolás Cabrera 13-15, Campus Cantoblanco, UAM 28049 Madrid, Spain; Instituto de Matemática e Estatística - IME/USP, Rua do Matão, 1010 - Cidade Universitária, São Paulo - SP, 05508-090, Brasil
Email: abad@icmat.es

P. Tradacete
Affiliation: Department of Mathematics, Universidad Carlos III de Madrid, 28911, Leganés, Madrid, Spain
Email: ptradace@math.uc3m.es

DOI: https://doi.org/10.1090/tran/6636
Keywords: Unconditional basis, random unconditional convergence.
Received by editor(s): September 23, 2014
Received by editor(s) in revised form: December 19, 2014
Published electronically: March 18, 2016
Article copyright: © Copyright 2016 American Mathematical Society