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Absolute summability of infinite series. (English) Zbl 0851.40004

Summary: It is shown in [C. Orhan, Bull. Inst. Math., Acad. Sin. 15, 433-437 (1987; Zbl 0649.40009)] that if a normal matrix \(A\) satisfies some conditions then \(|C, 1|_k\) summability implies \(|A|_k\) summability where \(k\geq 1\). In the present paper, we consider the converse implication.

MSC:

40F05 Absolute and strong summability

Citations:

Zbl 0649.40009
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Full Text: DOI

References:

[1] Flett, T. M., On an extension of absolute summability and theorems of Littlewood and Paley, Proc. London Math. Soc., 7, 113-141 (1957) · Zbl 0109.04402 · doi:10.1112/plms/s3-7.1.113
[2] Cooke R G,Infinite Matrices and Sequence Spaces (Macmillan) (1950) · Zbl 0040.02501
[3] Kogbetliantz, E., Sur les series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math., 49, 234-256 (1925)
[4] Orhan, C., On absolute summability, Bull. Inst. Math. Acad. Sinica, 15, 433-437 (1987) · Zbl 0649.40009
[5] Orhan, C., On equivalence of summability methods, Math. Slovaca, 40, 171-175 (1990) · Zbl 0736.40002
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