Pre-Quasi Simple Banach Operator Ideal Generated by s- Numbers
Bakery, Awad A.; Abou Elmatty, Afaf R.;
Abstract
Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s-numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s-numbers is simple Banach space.
Other data
Title | Pre-Quasi Simple Banach Operator Ideal Generated by s- Numbers | Authors | Bakery, Awad A. ; Abou Elmatty, Afaf R. | Issue Date | 1-Jan-2020 | Journal | Journal of Function Spaces | ISSN | 23148896 | DOI | 10.1155/2020/9164781 | Scopus ID | 2-s2.0-85085682192 |
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