On the properties of complemented basic sequences in block spaces of Kothe`s type

The paper contains some remarks on the properties of special basic sequences of the elements which span complemented subspaces in the Frechet spaces of the class that can be considered as a generalization of the well-known class of Kothe sequnce spaces. We discuss the question of characterization of these sequences of elements in block-Kothe spaces and survey the available results in this area. Some open problems are posed, and the connection of the topic under study is addressed with the problem of the isomorphic classification of Kothe spaces.