Matrix methods and the property of stretchings

Keagy, T. A.

doi:10.1090/S0002-9939-1987-0911030-9

Matrix methods and the property of stretchings
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by T. A. Keagy

Proc. Amer. Math. Soc. 101 (1987), 667-670

DOI: https://doi.org/10.1090/S0002-9939-1987-0911030-9

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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 $t$.

References

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