Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-11T01:47:12.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Conditions for Matrices to be Bounded Operators on lp

Published online by Cambridge University Press:  20 November 2018

David Borwein
David Borwein*
Affiliation:
Department of Mathematics University of Western Ontario London, Ontario N6A 5B7
Rights & Permissions [Opens in a new window]

Abstract

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.

The two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on ${{l}_{p}}$. The theorems are applied to Nörlund and weighted mean matrices.

Keywords

47B3747A3040G05Triangular matricesNörlund matricesweighted meansoperators on lp
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 10 - 14
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Borwein, D., Generalized Hausdorff matrices as bounded operators on lp. Math. Z. 183 (1983), 483–487.Google Scholar
2. Borwein, D., Nörlund operators on lp. Canad. Math. Bull. 36 (1993), 8–14.Google Scholar
3. Borwein, D. and Cass, F. P., Nörlund matrices as bounded operators on lp. Arch.Math. 42 (1984), 464–469.Google Scholar
4. Borwein, D. and Jakimovski, A., Matrix Operators on lp. Rocky Mountain J. Math. 9 (1979), 463–476.Google Scholar
5. Borwein, D. and Gao, X., Generalized Hausdorff and weighted mean matrices as operators on lp. J. Math. Anal. Appl. 178 (1993), 517–528.Google Scholar
6. Cartlidge, J. M., Weighted Mean Matrices as Operators on lp. Ph. D. thesis, Indiana University, 1978.Google Scholar
7. Cass, F. P. and Kratz, W., Nörlund and weighted mean matrices as operators on lp. RockyMountain J. Math. 20 (1990), 59–74.Google Scholar
8. Davies, G. S. and Petersen, G. M., On an inequality of Hardy's (II). Quart. J. Math. Oxford 15 (1964), 35–40.Google Scholar
9. Johnson, P. D. jr., Mohapatra, R. N. and D. Ross, Bounds for the operator norms of some Nörlund matrices. Proc. Amer. Math. Soc. 124 (1996), 543–547.Google Scholar
10. Németh, J., Generalizations of the Hardy-Littlewood inequality. Acta Sci. Math. (Szeged) 32(1971), 259– 299.Google Scholar