Multirectangular characteristics for Köthe power spaces of the second kind

Isomorphisms of the so-called Köthe power spaces of the second kind are considered. These spaces are determined by a pair of sequences of positive numbers. Counting functions for a pair of sequences ($m$-rectangular characteristics of the corresponding Köthe space of the second kind) are introduced. They are shown to be invariant under isomorphisms. The proof is based on the construction of special compound invariants suitable for the class of spaces under consideration. New results on the linear topological structure of spaces of analytic functions in multicircular domains are obtained as an application.
Bibliography: 29 titles.