Pairs of finite-type power series spaces

Abstract

Let be sequences of positive numbers. We study the problem on isomorphic classification of pairs(Error rendering LaTeX formula). For this purpose we introduce the sequence of so-called m-rectangle characteristics . It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite type power series spaces. Using some new linear topological invariants (compound invariants) we prove that m-rectangle characteristics are invariant on the class of such pairs. Some applications to pairs of spaces of analytic functions are considered.