Non-self-adjoint Operator Algebra Of The Lie Ideals And Conjugated Atoms On The Csl Algebra Of Invariant Subspaces Do Not Pay The Diagonal Ideal

Completely distributive and commutative subspace lattice(CDCSL for short) al-gebra is an important class of non-selfadjoint reflexive operator algebras. In this paper,we will study the connection between Lie ideals and conjugation-invariant subspacesin CDCSL algebras. For this sake, a class of lattices called V-generators dense latticesare introduced, which strictly include the class of completely distributive lattices andthe class of Pentagon lattices. When L is a V-generators dense and commutativelattice(GDCSL for short), a description for the Lie ideal [AlgL:I] is given.In chapter 1, we introduce the background and preliminary, and summarizes themain results of this thesis.In chapter 2, we describes the construction of atomic-diagonal disjoint ideals incommutative subspace lattice(CSL for short) algebras.In Chapter 3, we first describe the construction of the Lie ideal [AlgL: I] in GD-CSL algebras. Further, we show that Lie ideals and conjugation-invariant subspacesare equivalent for CDCSL algebras.