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Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness. (English) Zbl 1171.40002
Recently C. Adydin and F. Başar [Appl. Math. Comput. 157, No. 3, 677–693 (2004; Zbl 1072.46007)] studied the matrix domain of a triangular matrix in the sets of sequences that are (i) summable to zero, (ii) summable and (iii) bounded by the Cesàro method of order one. I. J. Maddox [J. Lond. Math. Soc. 43, 285-290 (1968; Zbl 0155.38802)] introduced and studied the above-mentioned class of sequences by the strong Cesàro method of order 1 with index $p$, $p\ge 1$. Here the authors discuss the class of sequences studied by C. Adydin and F. Basar for the strong Cesàro method of order 1 with index $p$, $p\ge 1$. They also determine the $\beta$-duals of the spaces studied and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.
##### MSC:
 40C05 Matrix methods in summability 40H05 Functional analytic methods in summability
##### References:
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