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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Matrix methods and the property of stretchings


Author: T. A. Keagy
Journal: Proc. Amer. Math. Soc. 101 (1987), 667-670
MSC: Primary 40C05
DOI: https://doi.org/10.1090/S0002-9939-1987-0911030-9
MathSciNet review: 911030
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Abstract: D. F. Dawson has proved that if $ x$ is a sequence and $ A$ is a matrix with convergent row sums, then there exist a stretching $ z$ of $ x$ and a row finite matrix $ B$ such that $ Ay$ and $ By$ converge or diverge together for each stretching $ y$ of $ z$. An extension of this result is used to answer a question proposed by D. Gaier regarding the conditions necessary for a matrix $ A$ to have the property that if $ x$ is a sequence with finite limit point $ t$, then $ A$ sums a stretching of $ x$ to $ t$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0911030-9
Keywords: Regular, segment, stretching
Article copyright: © Copyright 1987 American Mathematical Society