Some distinguished subspaces of domains of operator valued matrices (Q1262483)

On the base of FH-spaces one may generalize FK-space-theory founded by K. Zeller about 1950 from the case of sequence spaces of scalar sequences to the case of sequence spaces over a Fréchet-space X. Using this idea, \textit{M. S. Ramanujan} [Publ. Ramanujan Inst. 1, 145-153 (1969; Zbl 0196.081)] and \textit{L. W. Baric} [Stud. Math. 39, 165-180 (1971; Zbl 0212.456)] considered domains of operator valued matrices as generalized FK- spaces, which are called FK(X)-spaces in the present paper; they generalized some results in summability in connection with perfectness and conullity. In section 2 of the present paper we give a short introduction into the theory of FK(X)-spaces and in section 3 we generalize some important results on distinguished subsets of matrix domains due to \textit{A. Wilansky} [J. Anal. Math. 12, 327-350 (1964; Zbl 0127.027)] from the case of complex matrices to the case of operator valued matrices.