Geodesic
Simple Conditions for Matrices to be Bounded Operators on lp
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 10-14

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

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.
DOI : 10.4153/CMB-1998-002-7
Mots-clés : 47B37, 47A30, 40G05, Triangular matrices, Nörlund matrices, weighted means, operators on lp 
Borwein, David. Simple Conditions for Matrices to be Bounded Operators on lp. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 10-14. doi: 10.4153/CMB-1998-002-7
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[1] 1. Borwein, D., Generalized Hausdorff matrices as bounded operators on lp. Math. Z. 183 (1983), 483–487. Google Scholar

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

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

[4] 4. Borwein, D. and Jakimovski, A., Matrix Operators on lp. Rocky Mountain J. Math. 9 (1979), 463–476. Google Scholar

[5] 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] 6. Cartlidge, J. M., Weighted Mean Matrices as Operators on lp. Ph. D. thesis, Indiana University, 1978. Google Scholar

[7] 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] 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] 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] 10. Németh, J., Generalizations of the Hardy-Littlewood inequality. Acta Sci. Math. (Szeged) 32(1971), 259– 299. Google Scholar

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