Operators Between Matrix Domains

In this chapter, we apply the results of the previous chapters to characterize matrix transformations on the spaces of generalized weighted means and on matrix domains of triangles in BK spaces. We also establish estimates or identities for the Hausdorff measure of noncompactness of matrix transformations from arbitrary BK spaces with AK into c, $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 , and also from the matrix domains of an arbitrary triangle in $$\ell _{p}$$ ℓ p , c and $$c_{0}$$ c 0 into c, $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 . Furthermore we determine the classes of compact operators between the spaces just mentioned. Finally we establish the representations of the general bounded linear operators from c into itself and from the space $$bv^{+}$$ b v + of sequences of bounded variation into c, and the determination of the classes of compact operators between them.