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Zbl 0653.40001
Connor, J.S.
The statistical and strong p-Cesaro convergence of sequences.
(English)
[J] Analysis 8, No.1-2, 47-63 (1988). ISSN 0174-4747

Summary: It is shown that if a sequence is strongly p-Cesàro summable or $w\sb p$ convergent for $0<p<\infty$ then the sequence must be statistically convergent and that a bounded statistically convergent sequence must be $w\sb p$ 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.
MSC 2000:
*40A05 Convergence of series and sequences
40D25 Inclusion theorems, etc.
40D09 Structure of summability fields
40C05 Matrix methods in summability
40H05 Functional analytic methods in summability

Keywords: Cesàro convergence; bounded statistically convergent sequence; locally convex FK space; Nörlund-type means

Cited in: Zbl 0907.40002 Zbl 0726.40009

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