Matrix transformations between the sequence space BVP and certain BK spaces

Abstract

In this paper, we characterize matrix transformations between the sequence space bv p (1 < p < ∞) and certain BK spaces. Furthermore, we apply the Hausdorff measure of noncompactness to give necessary and sufficient conditions for a linear operator between these spaces to be compact.

Integrated and Differentiated Sequence Spaces and Weighted Mean

“…for all k, n ∈ N, where E = (e nk ) is defined by (18) Theorem 3.3. We define the matrix F = (f nk ) as…”

Compact operators into the spaces of strongly summable and bounded sequences

“…An important application of the Hausdorff measure of noncompactness of bounded linear operators between Banach spaces is the characterisation of compact matrix transformations between BK spaces [11][12][13][14][15][16][17][18][19][20][21][22]. The characterisations of compact matrix operators between the classical sequence spaces in almost all cases can be found in [23].…”

Ordinary, absolute and strong summability and matrix transformations

“…Further results concerning the characterizations of matrix transformations and compact operators between the matrix domains of triangles can be found in [14,15,16,17,18].…”

“…We write T for the set of all strictly increasing sequences t = (t ν ) ∞ ν=0 of integers such that for each ν there is one and only one t ν ∈ I ν . Further results on matrix transformations and compact operators between mixed norm spaces can be found in [14,8,15,16].…”