Klassen von Matrizenabbildungen in FK-Räumen. (Classes of matrix maps in FK-spaces) (Q1097497)

Let X and Y be sequence spaces. Then the class of all infinite complex matrices that map X into Y is denoted by (X,Y). For arbitrary p-normed FK spaces X, the characterization of each of the following classes is given: \((X,\ell_ 1)\), (X,bv), \((X,\gamma_{\infty})\), and if X is an arbitrary complete p-normed sequence space with basis \((e^{(k)}):(X,\gamma)\) and \((X,\gamma_ 0)\). Further for a certain class of reflexive sequence spaces Y, the classes \((\ell_ 1,Y)\), (bv,Y) and \((\gamma_{\infty},Y)\) are determined. Finally a few examples are given in order to illustrate how various classical results can easily be obtained from our general results.