Geodesic
The kernel of a~sequence obtained from a~given sequence with the aid of a~regular transformation
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 707-716

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The smallest set is found that contains the kernel of a sequence obtained from a sequence of elements $\{x_n\}$ of a Banach space with the aid of a regular transformation of the class $T(C,C')$. Here $T(C,C')$ is the set of complex matrices $(c_{nk}\equiv(a_{nk}+ib_{nk})$ satisfying the conditions $\varlimsup\limits_{n\to\infty}\sum_{k=1}^\infty|a_{nk}|=C\ge1$, $\varlimsup\limits_{n\to\infty}\sum_{k=1}^\infty|b_{nk}|=C'\ge0$. 
@article{MZM_1976_19_5_a5,
     author = {A. A. Shcherbakov},
     title = {The kernel of a~sequence obtained from a~given sequence with the aid of a~regular transformation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {707--716},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a5/}
}
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A. A. Shcherbakov. The kernel of a~sequence obtained from a~given sequence with the aid of a~regular transformation. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 707-716. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a5/