Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces

Abstract

The new sequence spaces X(r, s, t; ) for X ∈ {l ∞ , c, c 0 } have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces X(r, s, t; ) where X ∈ {l ∞ , c, c 0 , l p } (1 ≤ p < ∞), as derived by using generalized means. Further, we find the necessary and sufficient conditions for such operators to be compact by applying the Hausdorff measure of noncompactness. Finally, as applications we characterize some classes of compact operators between these new difference sequence spaces and some other BK-spaces.Keywords: sequence space; difference operators; matrix transformation; generalized means; compact operators; Hausdorff measure of noncompactness Preliminaries and backgroundThe study of sequence spaces has been very useful in many branches of analysis. Recently, some new sequence spaces have been defined by using matrix domain of a suitable matrix. Beside this, the Hausdorff measure of noncompactness is very useful in the classification of compact operators between Banach spaces.The difference sequence spaces were introduced for the first time by Kizmaz in []. Afterwards, many authors have introduced and studied some new sequence spaces defined by using the difference operator. In this paper we obtain some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on new difference sequence spaces defined by Manna et al. Further, we find the necessary and sufficient condi-