Geodesic
Summation of bounded sequences by regular positive matrices
Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 179-188.

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In terms of elements of regular positive discrete and semicontinuous matrices sufficient conditions are obtained that these matrices do not sum a given real,divergent, bounded sequence and, in particular, that the core of a given sequence coincides with the core of the sequence (function) transformed with the aid of a matrix. These conditions permit certain facts, some well-known and some new, on the theory of inefficient matrices to be obtained. 
@article{MZM_1973_13_2_a1,
     author = {N. A. Davydov},
     title = {Summation of bounded sequences by regular positive matrices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {179--188},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a1/}
}
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N. A. Davydov. Summation of bounded sequences by regular positive matrices. Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 179-188. http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a1/