(Strictly) Cyclic Algebras Of Operators And Their Reflexivety

In this paper, I investigated mainly the reflexivity of (strictly) cyclic subalgebras of operators, and also discussed some properties regarding their reflexivity. It can be divided into four sections.In the first part, I introduce the history of the reflexivity of operator algebras and some present results. I also introduce how the author came up with the thoughts of the thesis and the main results.In the second part, I discussed some properties regarding the reflexivity of cyclic subalgebras on a normed vector space. The 2-refiexivity and hyporeflexivity of cyclic subalgebras are attained, and the answers to Deddens's questions in reference document [19] are obtained partly.In the third part, I genelized one theorem of Lambert's from a Hilbert space to a semi-self-conjugate vector space, and some results of reflexivity are attained.In the fourth part, I discussed the algebraic reflexivity of a (strictly) cyclic linear transformation on a vector space.