Multiplication Operators on Cesàro-Orlicz Sequence Spaces

Abstract

Abstract. In this paper, we characterize the compact, invertible, Fredholm and closed range multiplication operators on Cesàro-Orlicz sequence spaces.

The essential norm of multiplication operators acting on Orlicz sequence spaces

“…Arora et al in [1] proved that a multiplication operator M u acting on Lorentz sequence spaces is compact if and only if u ∈ c 0 ; that is, if and only if u(n) → 0 as n → ∞. This last condition also characterize the compactness of this operator M u , acting on other Köthe sequence spaces such as Orlicz-Lorentz sequence spaces [2], Cesàro sequence spaces [7], Cesàro-Orlicz sequence spaces [9], among others. However, the characterization of compactness (and other properties) of multiplication operators acting on any Köthe sequence spaces is due to Ramos-Fernández and Salas-Brown [10] (see also [5] and [3]).…”

Multiplication Operators on Second Order Cesaro-Orlicz Sequence Spaces

“…After Lim and Lee [18] found the dual spaces of Cesàro-Orlicz sequence spaces Ces ϕ (N), Cui et al [19] and Damian [20] investigated some properties of these spaces. Later, the authors in [21] studied the multiplication operators on Cesàro-Orlicz sequence spaces.…”

On the Essential Norm of Multiplications Operators Acting on Cesàro Sequence Spaces

“…Arora et al in [6] show that a multiplication operator acting on Lorentz sequence spaces is compact if and only if ∈ 0 , that is, if and only if ( ) → 0 as → ∞. This last condition also characterizes the compactness of this operator , acting on other Banach sequence spaces such as Orlicz-Lorentz sequence spaces [10], Cesàro sequence spaces [11], Cesàro-Orlicz sequence spaces [12], among others. However, the above spaces are classified as Köthe sequence spaces and the characterization of compactness (and other properties) of multiplication operators acting on Köthe sequence spaces is due to Ramos-Fernández and Salas-Brown [13] (see also [14,15]).…”