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.


40F05 Absolute and strong summability


Zbl 0649.40009
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.