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

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DOI

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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     title = {Matrix {Operators} on lp to lq},
     journal = {Canadian mathematical bulletin},
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     year = {1994},
     volume = {37},
     number = {4},
     doi = {10.4153/CMB-1994-065-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-065-7/}
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