Geodesic
Summation of arbitrary series by Riesz methods
Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 541-550

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It is known (theorem of Agnew and Darevskii) that for each divergent real sequence $\{s_n\}$ and each real number $c$, there exists a $T$-method of summing $\{s_n\}$ to $c$. In this note it is shown that for each divergent sequence which is bounded above or below we can take the $T$-method in the above theorem to be a Riesz method. We also study Riesz summability of unbounded (above and below) sequences. 
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     author = {L. V. Grepachevskaya},
     title = {Summation of arbitrary series by {Riesz} methods},
     journal = {Matemati\v{c}eskie zametki},
     pages = {541--550},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a6/}
}
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L. V. Grepachevskaya. Summation of arbitrary series by Riesz methods. Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 541-550. http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a6/