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Weak statistical convergence and weak filter convergence for unbounded sequences

Kadets, Vladimir; Leonov, Alexander; Orhan, Cihan


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{
  "DOI": "10.1016/j.jmaa.2010.05.031", 
  "abstract": "For every weakly statistically convergent sequence (x(n)) with increasing norms in a Hilbert space we prove that sup(n) parallel to x(n)parallel to/root n < infinity This estimate is sharp We study analogous problem for sonic other types of weak filter convergence. in particular for the Erdos-Ulam filters, analytical P-filters and F-sigma filters We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm (C) 2010 Elsevier Inc. All rights reserved.", 
  "author": [
    {
      "family": "Kadets", 
      "given": " Vladimir"
    }, 
    {
      "family": "Leonov", 
      "given": " Alexander"
    }, 
    {
      "family": "Orhan", 
      "given": " Cihan"
    }
  ], 
  "container_title": "JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS", 
  "id": "25141", 
  "issue": "2", 
  "issued": {
    "date-parts": [
      [
        2010, 
        1, 
        1
      ]
    ]
  }, 
  "page": "414-424", 
  "title": "Weak statistical convergence and weak filter convergence for unbounded sequences", 
  "type": "article-journal", 
  "volume": "371"
}
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