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2-co-lacunary sequences in noncommutative symmetric Banach spaces


Authors: Fedor Sukochev and Dejian Zhou
Journal: Proc. Amer. Math. Soc. 148 (2020), 2045-2058
MSC (2010): Primary 46L52; Secondary 46L53, 46E30
DOI: https://doi.org/10.1090/proc/14862
Published electronically: January 13, 2020
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Abstract: We characterize noncommutative symmetric Banach spaces for which every bounded sequence admits either a convergent subsequence, or a $ 2$-co-lacunary subsequence. This extends the classical characterization, due to Räbiger.


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Additional Information

Fedor Sukochev
Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington 2052, Australia
Email: f.sukochev@unsw.edu.au

Dejian Zhou
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410083, People’s Republic of China
Email: zhoudejian@csu.edu.cn

DOI: https://doi.org/10.1090/proc/14862
Keywords: $2$ co-lacunary sequences, noncommutative symmetric spaces, noncommutative Khintchine inequality
Received by editor(s): June 8, 2019
Received by editor(s) in revised form: August 31, 2019, and September 7, 2019
Published electronically: January 13, 2020
Additional Notes: The second author is the corresponding author.
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society