Vol. 44, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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