ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

The author shows a characterization of a （unbounded） weakly filter convergent sequence which is parallel to that every weakly null sequence （xn） in a Banach space admits a norm null sequence （yn） with yn ∈ co（xk）k≥n for all n ∈ N. A version of the Radon-Riesz type theorem is also proved within the f...

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Bibliographic Details
Published in:Acta mathematica scientia 2016, Vol.36 (1), p.215-219
Main Author: 鲍玲鑫
Format: Article
Language:English
Subjects:
40A35
46B15
Banach space
filter convergence
Radon-Riesz property
statistical convergence
sz型
定理证明
巴拿赫空间
弱收敛
收敛序列
滤波器
过滤器
零序列
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Summary:The author shows a characterization of a （unbounded） weakly filter convergent sequence which is parallel to that every weakly null sequence （xn） in a Banach space admits a norm null sequence （yn） with yn ∈ co（xk）k≥n for all n ∈ N. A version of the Radon-Riesz type theorem is also proved within the frame of the filter convergence.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(15)30089-8