Vol. 44, No. 2, 1973

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Summability of subsequences and stretchings of sequences

David Fleming Dawson

Vol. 44 (1973), No. 2, 455–460

In 1943 R. C. Buck gave a summability characterization of real convergent sequences by showing that a real sequence x is convergent if there exists a regular matrix summability method which sums every subsequence of x. In 1944 R. P. Agnew generalized Buck’s result by showing that if x is a bounded complex sequence and A is a regular matrix, then there exists a subsequence y of x such that every limit point of x is a limit point of Ay. In the present paper a theorem concerning “stretchings” of sequences is proved; and from this theorem, summability characterizations of several classes of sequences are obtained, together with an extension of Agnew’s result.

Mathematical Subject Classification 2000
Primary: 40C05
Revised: 7 December 1971
Published: 1 February 1973
David Fleming Dawson