Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T00:31:25.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Submethods Of Regular Matrix Summability Methods

Published online by Cambridge University Press:  20 November 2018

Casper Goffman  and
G. M. Petersen
Casper Goffman
Affiliation:
University of Oklahoma
G. M. Petersen
Affiliation:
University of Oklahoma
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.

By a submethod of a regular matrix method A we mean a method (see 1 or 3) whose matrix is obtained by deleting a set of rows from the matrix A. We establish a one-one correspondence between the submethods of A and the points of the interval 0 < ξ ≤We designate the submethod which corresponds to 𝞷 by A (𝞷) and are accordingly able to speak of sets of submethods of measure 0, of the first category, etc.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 40 - 46
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Cooke, R. G., Infinite Matrices and Sequence Spaces (London, 1950).Google Scholar
2. Halmos, P. R., Measure Theory (New York, 1950).Google Scholar
3. Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
4. Hill, J. D., Summability of sequences of 0's and 1's, Annals of Math., 46 (1945), 556–562.Google Scholar
5. Hill, J. D., Remarks on the Borelproperty, Pacific J. Math., 4 (1954), 227–242.Google Scholar
6. Lorentz, G. G., A contribution to the theory of divergent series, Acta Math., 80 (1948), 167–190.Google Scholar

A correction has been issued for this article:

Correction to the Paper*