Geodesic
Noneffectiveness of a class of regular matrices
Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 361-364 
G. A. Mikhalin. Noneffectiveness of a class of regular matrices. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 361-364. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a0/
@article{MZM_1974_16_3_a0,
     author = {G. A. Mikhalin},
     title = {Noneffectiveness of a~class of regular matrices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--364},
     year = {1974},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a0/}
}
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We show that if a sequence $\{\varepsilon_n\}$ is such that $\varepsilon_1>\varepsilon_2\ge\varepsilon_3\ge\dots$, $\sum_{n=1}^\infty\varepsilon_n=1$, then for any bounded sequence $\{S_n\}$ the equation $\lim\limits_{n\to\infty}\sum_{k=1}^n\varepsilon_{n+1-k}S_k=S$ implies the equation $\lim\limits_{n\to\infty}S_n=S$. This theorem generalizes a theorem of N. A. Davydov [2].