Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T14:49:05.238Z Has data issue: false hasContentIssue false
  • English
  • Français

Inclusion sets of regular summability matrices. III

Published online by Cambridge University Press:  24 October 2008

J. W. Baker  and
G. M. Petersen
J. W. Baker
Affiliation:
University College, Swansea, and University of Canterbury, Christchurch
G. M. Petersen
Affiliation:
University College, Swansea, and University of Canterbury, Christchurch
Get access Rights & Permissions [Opens in a new window]

Extract

Let A = (am, n) be a (regular summability) matrix. Then will denote the set of bounded sequences which are summed by A. If {Ai} (i = 1, 2, …, N) is a finite set of such matrices, and if consists of every bounded sequence then we shall say that the matrices span the bounded sequences. Ifx = {xn} belongs to then we denote the value to which A sums x by A-lim x. If y = {yn} is any sequence, then the A-transform of y (if it exists) is the sequence {Aμ(y)}, where

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 389 - 394
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baker, J. W. and Petersen, G. M.Inclusion of sets of regular summability matrices. Proc. Cambridge Philos. Soc. 60 (1964), 705–712.CrossRefGoogle Scholar
(2)Baker, J. W. and Petersen, G. M.Inclusion of sets of regular summability matrices. II. Proc. Cambridge Philos. Soc. 61 (1965), 381–394.CrossRefGoogle Scholar
(3)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(4)Lorentz, G. G. and Zeller, K.Über paare von Limitierungsverfahren. Math. Z. 68 (1958), 428–438.CrossRefGoogle Scholar
(5)Petersen, G. M.On pairs of summability matrices. Quart. J. Math. Oxford Ser. (2), 16 (1965), 72–76.CrossRefGoogle Scholar