ON M-RECTANGLE CHARACTERISTICS AND ISOMORPHISMS OF MIXED (F)-, (DF)- SPACES

Can Deha Karıksız
Mathematics, Ph.D. Dissertation, 2014 

Thesis Jury
Prof. Dr. Vyacheslav P. Zakharyuta (Thesis Supervisor), Prof. Dr. Aydın Aytuna, Assoc. Prof. Dr. Mert Çağlar, Prof. Dr. Tosun Terzioğlu, Prof. Dr. Murat Yurdakul

Date &Time: January 13th, 2014 - 15:00

Place: Sabancı Üniversitesi Karaköy Minerva Palas

Keywords:  linear topological invariants, compound invariants, m-rectangle characteristics, mixed (F)-, (DF)- spaces, quasi-equivalence of bases.

Abstract

In this thesis, we consider problems on the isomorphic classification and quasi-equivalence 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 defining 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 definitions 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 spaces of finite type and a (DF)- power series spaces of infinite type, under some equivalence. From these invariances, we obtain the quasi-equivalence of absolute bases in the spaces of the same class that are Montel and quasidiagonally isomorphic to their Cartesian square.