Abstract. In this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces. Introduction and preliminariesLet N be the set of positive integers. The Cesàro sequence space Cespl 2 pNqq is defined asThe space Cespl 2 pNqq is a Banach space under the normCesàro sequence spaces Let u : X Ñ C be a function such that u.f P Cespl 2 pNqq for every f P Cespl 2 pNqq. Then we can define a multiplication transformation M u : Cespl 2 pNqq Ñ Cespl 2 pNqq by M u f " u.f, @ f P Cespl 2 pNqq.

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

In this paper, we introduce some [Formula: see text]-convergence spaces of double difference sequences of interval numbers with Musielak–Orlicz function [Formula: see text] over [Formula: see text]-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. Furthermore, we study [Formula: see text]-statistical convergence of double difference sequences of interval numbers.

The compact, invertible, Fredholm, and closed range composition operators are characterized. We also make an effort to compute the essential norm of composition operators on the Cesàro function spaces.