Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces

Abstract: This Licentiate thesis consists of an introduction and three papers, which deal with some spaces of infinite matrices. In the introduction we give an overview of the area that serves as a frame for  the rest of the thesis. In Paper 1 we introduce the space $B_w(ell^2)$ of linear (unbounded) operators on $ell^2$ which map decreasing sequences from $ell^2$ into sequences from $ell^2$ and we find some classes of operators belonging either to $B_w(ell^2)$ or to the space of all Schur multipliers on $B_w(ell^2)$. In Paper 2 we further continue the study of the space $B_w(ell^p)$ in the range $1