Compact operators

Abstract

In this dissertation, we have dealt with the compact operators, these kind of operators play a fondamental role in mathematics and they are used to prove a lot of fondamental theorems in different mathematic subfields . This research consists of three main chapters. The first chapter was about the Hilbert spaces and theire properties and it was also about orthogonality and orthonormality. The second one discusses the operators and theire theorems and properties, it also discusses the adjoint of an operator and its properties and definitions. The third one covers this research object, compact operators, we have dealt in this chapter with the most important theorems and basics of the compact operators. Eventually i hope that i succeeded in presenting this dissertation throughly and simtly.