Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T16:48:20.164Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximation in Bounded Summability Fields

Published online by Cambridge University Press:  20 November 2018

J. D. Hill  and
W. T. Sledd
J. D. Hill
Affiliation:
Michigan State University, East Lansing, Michigan
W. T. Sledd
Affiliation:
Michigan State University, East Lansing, Michigan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with several related properties of bounded summability fields of regular, real matrices. For a matrix A = (ank) and a sequence x = {xn}, we write formally

We denote by m the space of bounded real sequences, and by A* the bounded summability field

of A. The strong summability field of A is the set

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 410 - 415
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Brauer, G., Evaluation of product sequences by matrix methods, Amer. Math. Monthly, 63 1956), 323–326.Google Scholar
2. Henriksen, M., Multiplicative summability methods and the Stone-Cech compactification, Math. Z., 71 (1959), 427–435.Google Scholar
3. Henriksen, M. and Isbell, J. R., Multiplicative summability methods and the Stone-Cech compactification, Abstract 608–611, Notices Amer. Math. Soc, 11 (1964), 90.Google Scholar
4. Schur, I., Über lineare Transformationen in der Théorie der unendlichen Reihen, J. Reine Angew. Math., 151 (1921), 79–111.Google Scholar