Abstract
We study the ideal of all bounded linear operators between any arbitrary Banach spaces whose sequence of approximation numbers belong to the generalized Cesaro sequence space and Orlicz sequence space , when , ; our results coincide with that known for the classical sequence space .
Highlights
By L(X, Y ), we denote the space of all bounded linear operators from a normed space X
The set of natural numbers will denote by N = {, . . .} and the real numbers by R
First we prove that every finite mapping T ∈
Summary
By L(X, Y ), we denote the space of all bounded linear operators from a normed space X into a normed space Y. We call such space Eρ a pre modular special space of sequences if there exists a function ρ : E → [o, ∞[, satisfies the following conditions: (i) ρ(x) ≥ ∀x ∈ Eρ and ρ(θ ) = , where θ is the zero element of E, (ii) there exists a constant l ≥ such that ρ(λx) ≤ l|λ|ρ(x) for all values of x ∈ E and for any scalar λ, (iii) for some numbers k ≥ , we have the inequality ρ(x + y) ≤ k(ρ(x) + ρ(y)), for all x, y ∈ E, (iv) if |xn| ≤ |yn|, for all n ∈ N ρ((xn)) ≤ ρ((yn)), (v) for some numbers k we have the inequality ρ((xn))
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
