Geodesic
Relation between summability and absolute summability by Ces\`aro means of complex order
Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 13-18

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It is proved that if a series is absolute summable by a Cesàro $(C,\alpha)$ method, then it is summable $(C,\beta)$ for any $\beta$, such that $\mathrm{Re}\,\alpha=\mathrm{Re}\,\beta>-1$. 
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     author = {I. I. Volkov},
     title = {Relation between summability and absolute summability by {Ces\`aro} means of complex order},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {1},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a1/}
}
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I. I. Volkov. Relation between summability and absolute summability by Ces\`aro means of complex order. Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 13-18. http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a1/