Geodesic
CLASSES OF SEQUENTIALLY LIMITED OPERATORS
Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 573-586

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DOI

The purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals. 
FOURIE, JAN H.; ZEEKOEI, ELROY D. CLASSES OF SEQUENTIALLY LIMITED OPERATORS. Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 573-586. doi: 10.1017/S0017089515000348
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     author = {FOURIE, JAN H. and ZEEKOEI, ELROY D.},
     title = {CLASSES {OF} {SEQUENTIALLY} {LIMITED} {OPERATORS}},
     journal = {Glasgow mathematical journal},
     pages = {573--586},
     year = {2016},
     volume = {58},
     number = {3},
     doi = {10.1017/S0017089515000348},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000348/}
}
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