Decomposition and properties of a spectrum

Abstract

The study sought to show the relationships of the decomposed subsets of the spectrum by use of inclusions. In operator Theory, we study of linear operator on function spaces acting on vector spaces of functions. Since an element of s(A) (ie spectrum of A), is a spectrum value of A, we need to investigate more about these elements of A, by decomposing the spectrum to various subsets. From the decomposed subsets of the spectrum, we study the properties of spectrum to give an insight of deeper understanding of the spectrum. The deductions from the proofs of Theorems, propositions, Lemmas and corollaries will help to expose the properties being investigated.