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

References

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