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Matrix Operators on lp to lq

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Xiaopeng Gao
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario London, Ontario N6A 5B7 e-mail:, dborwein@uwo.ca
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Abstract

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Workable necessary and sufficient conditions for a non-negative matrix to be a bounded operator from lp to lq when 1 < q ≤ p < ∞ are discussed. Alternative proofs are given for some known results, thereby filling a gap in the proof of the case p = q of a result of Koskela's. The case 1 < q < p < ∞ of Koskela's result is refined, and a weakened form of the Vere-Jones conjecture concerning matrix operators on lp is shown to be false.

Keywords

47B3747A30operators on lp to lqinfinite matrices

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 448 - 456
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Borwein, D. and Jakimovski, A., Matrix operators on lp , Rocky Mountain J. Math. 9(1979), 463–476.Google Scholar
2. Borwein, D., Generalized Hausdorff matrices as bounded operators on lp , Math. Z. 183(1983), 483–487.Google Scholar
3. Borwein, D. and Cass, F. P., Norlund matrices as bounded operators on lp , Arch. Math. 42(1984), 464–469.Google Scholar
4. Borwein, D., Nörlund operators on lp , Canad. Math. Bull. (1) 36(1993), 8–14.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. Cass, F. P. and Kratz, W., Nörlund and weighted mean matrices as bounded operators on lp , Rocky Mountain J. Math. 20(1990), 59–74.Google Scholar
7. Ladyženskii, L. A., Über ein Lemma von Schur, Latviisk Mat. Ežegodnik 9(1971), 139–150.Google Scholar
8. Koskela, M., A characterization of non-negative matrix operators on lp to lq with ∞ > p > q > 1, Pacific J. Math. 75(1978), 165–169.+p+>+q+>+1,+Pacific+J.+Math.+75(1978),+165–169.>Google Scholar
9. Szeptycki, P., Dissertationes Mathematicae, Warsaw, Notes on Integral Transformations, 1984.Google Scholar
10. Vere- Jones, D., Ergodic properties of non-negative matrices-II, Pacific J. Math. 26(1968), 601–620.Google Scholar