On m-rectangle characteristics and isomorphisms of mixed (F)-, (DF)-spaces

Official URL: http://risc01.sabanciuniv.edu/record=b1558937 (Table of Contents)

In this thesis, we consider problems on the isomorphic classification and quasiequivalence properties of mixed (F)-, (DF)- power series spaces which, up to isomorphisms, consist of basis subspaces of the complete projective tensor products of power series spaces and (DF)- power series spaces. Important linear topological invariants in this consideration are the m-rectangle characteristics, which compute the number of points of the de ning sequences of the mixed (F)-, (DF)- power series spaces, that are inside the union of m rectangles. We show that the systems of m-rectangle characteristics give a complete characterization of the quasidiagonal isomorphisms between Montel spaces that are in certain classes of mixed (F)-, (DF)- power series spaces under proper de nitions of equivalence. Using compound invariants, we also show that the m-rectangle characteristics are linear topological invariants on the class of mixed (F)-, (DF)- power series spaces that consist of basis subspaces of the complete projective tensor products of a power series space of nite type and a (DF)- power series space of in nite type. From these invariances, we obtain the quasiequivalence of absolute bases in the spaces of the same class that are Montel and quasidiagonally isomorphic to their Cartesian square.