Matrix transformations on mixed paranorm spaces

Abstract

Recently the concept of mixed norm spaces was generalized to that of the mixed paranorm spaces [l(r),lp]<k(v)>. Here we determine the classes of matrix transformations from [l(r),lp]<k(v)> into the spaces of bounded, convergent and null sequences, and into the spaces of all bounded, convergent and absolutely convergent series. We also obtain many correponding known results for mixed norm spaces as special cases and visualize some neighborhoods in the spaces [l(r),lp]<k(v)>.