Compact matrix operators on a new sequence space related to ℓ p $\ell_{p}$ spaces

Abstract

Abstract In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space ℓ p ( r , s , t ; B ( m ) ) $\ell_{p}(r,s,t;B^{(m)})$ which is related to ℓ p $\ell_{p}$ spaces. By applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact. Further, we study some geometric properties of this space.

Keywords

• BK space
• matrix transformation
• Hausdorff measure of noncompactness
• compact operator
• geometric properties