Pairs of finite-type power series spaces

Abstract

Let $a=(a_i), a_i→∈fty,λ=(λ_i)$ be sequences of positive numbers. We study the problem on isomorphic classification of pairs $F=(K(\exp(-\frac{1}{a_i)),K(\exp(-\frac{1}{p}a_i+λ_i)))$. For this purpose we introduce the sequence of so-called m-rectangle characteristics $\mu_m^F$. 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.