Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers. (15th May 2020) - 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 S E X, Y ≔ T ∈ L X, Y : s n T n = 0 ∞ ∈ E of the class S E form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal S E, 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.