ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

doi:10.1016/S0252-9602(15)30089-8

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 215-219.doi: 10.1016/S0252-9602(15)30089-8

ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

鲍玲鑫

School of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China

收稿日期:2014-10-14 修回日期:2015-01-03 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Lingxin BAO,E-mail:bolingxmu@sina.com
基金资助:
The author was partially supported by the Natural Science Foundation of China(11426061, 11501108) and the Natural Science Foundation of Fujian province(2015J01579).

ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

Lingxin BAO

School of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China

Received:2014-10-14 Revised:2015-01-03 Online:2016-01-30 Published:2016-01-30
Supported by:
The author was partially supported by the Natural Science Foundation of China(11426061, 11501108) and the Natural Science Foundation of Fujian province(2015J01579).

摘要/Abstract

摘要：

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

关键词: statistical convergence, filter convergence, Radon-Riesz property, Banach space

Abstract:

Key words: statistical convergence, filter convergence, Radon-Riesz property, Banach space

中图分类号:

40A35

鲍玲鑫. ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM[J]. 数学物理学报(英文版), 2016, 36(1): 215-219.

Lingxin BAO. ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM[J]. Acta mathematica scientia,Series B, 2016, 36(1): 215-219.

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ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

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