Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (1): 215-219.doi: 10.1016/S0252-9602(15)30089-8

• Articles • Previous Articles     Next Articles

ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

Lingxin BAO   

  1. 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).

Abstract:

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)kn for all n∈N.A version of the Radon-Riesz type theorem is also proved within the frame of the filter convergence.

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

CLC Number: 

  • 40A35
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