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Weak statistical convergence and weak filter convergence for unbounded sequences

Kadets, Vladimir; Leonov, Alexander; Orhan, Cihan


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        "affiliation": "Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine", 
        "name": "Kadets, Vladimir"
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        "affiliation": "Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine", 
        "name": "Leonov, Alexander"
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        "affiliation": "Ankara Univ, Fac Sci, Dept Math, TR-06100 Ankara, Turkey", 
        "name": "Orhan, Cihan"
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    "description": "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.", 
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