Pairs of finite-type power series spaces


Let a=(a<sub>i</sub>), a_i→∈fty,λ=(λ<sub>i</sub>) 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 \mu<sub>m</sub><sup>F</sup>. 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.

DOI Code: 10.1285/i15900932v17p121

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