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.