Geodesic
Matrix Operators on lp to lq
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 448-456

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1994-065-7
Mots-clés : 47B37, 47A30, operators on lp to lq, infinite matrices 
Borwein, David. Matrix Operators on lp to lq. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 448-456. doi: 10.4153/CMB-1994-065-7
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[1] 1. Borwein, D. and Jakimovski, A., Matrix operators on l , Rocky Mountain J. Math. 9(1979), 463–476. Google Scholar

[2] 2. Borwein, D., Generalized Hausdorff matrices as bounded operators on l , Math. Z. 183(1983), 483–487. Google Scholar

[3] 3. Borwein, D. and Cass, F. P., Norlund matrices as bounded operators on l , Arch. Math. 42(1984), 464–469. Google Scholar

[4] 4. Borwein, D., Nörlund operators on l , Canad. Math. Bull. (1) 36(1993), 8–14. Google Scholar

[5] 5. Borwein, D. and Gao, X., Generalized Hausdorff and weighted mean matrices as operators on l , J. Math. Anal. Appl. 178(1993), 517–528. Google Scholar

[6] 6. Cass, F. P. and Kratz, W., Nörlund and weighted mean matrices as bounded operators on l , Rocky Mountain J. Math. 20(1990), 59–74. Google Scholar

[7] 7. Ladyženskii, L. A., Über ein Lemma von Schur, Latviisk Mat. Ežegodnik 9(1971), 139–150. Google Scholar

[8] 8. Koskela, M., A characterization of non-negative matrix operators on l to l with ∞ &gt; p &gt; q &gt; 1, Pacific J. Math. 75(1978), 165–169. +p+&amp;gt;+q+&amp;gt;+1,+Pacific+J.+Math.+75(1978),+165–169.&amp;gt;Google Scholar

[9] 9. Szeptycki, P., Dissertationes Mathematicae, Warsaw, Notes on Integral Transformations, 1984. Google Scholar

[10] 10. Vere- Jones, D., Ergodic properties of non-negative matrices-II, Pacific J. Math. 26(1968), 601–620. Google Scholar

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