On operators and complemented subspaces in the Köthe spaces determined by sparse matrices (Q1921848)

Any continuous linear operator \(T\) in a lacunary power series space generated by the system \((Z^{n_k})\), \(\lim_k {n_k\over n_{k+1}}= 0\), admits a representation \(T= J+K\), where the matrix of \(J\) (related to \((Z^{n_k})\)) may have nonzero entries only on the diagonal and \(K\) is a compact operator in the topology of uniform convergence on compact subsets of the unit disc. In the paper, a class of block Köthe spaces such that each continuous operator in each space of the class admits the above-like representation. In a sense, this is a generalization of a number of earlier results in this direction.