On Reducibility And Quasireducibility Of Operators In Hilbert Spaces

Abstract

In this dissertation, we study invariant, reducing and hyp erinvariant subspaces and how they play a key role in the study of reducibility and quasireducibility of op erators. We also consider some equivalence relations and characterize op erators in such equivalence relations and investigate which of the equivalence relations preserve reducibility and quasireducibility. The structure and relationship of invariant and hyp erinvariant lattices for some classes of op erators are investigated. The isomorphic lattices of similar and unitarily equivalent op erators are also discussed.