The statistical and strong p-Cesaro convergence of sequences. (English) Zbl 0653.40001

Summary: It is shown that if a sequence is strongly p-Cesàro summable or \(w_ p\) convergent for \(0<p<\infty\) then the sequence must be statistically convergent and that a bounded statistically convergent sequence must be \(w_ p\) convergent for any p, \(0<p<\infty\). It is also shown that the statistically convergent sequences do not form a locally convex FK space. A characterization of conservative matrices which map the bounded statistically convergent sequences into convergent sequences is given and applied to Nörlund and Nörlund-type means.


40A05 Convergence and divergence of series and sequences
40D25 Inclusion and equivalence theorems in summability theory
40D09 Structure of summability fields
40C05 Matrix methods for summability
40H05 Functional analytic methods in summability
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