Spectral Theory Of Linear Operators

Spectral theory of linear operators is one of the basic theories in modern mathematics. It is widely used in mathematics, physics, engineering and so on. A great development has been achieved on the spectral theory of linear operators. Before we research the new theory, we should learn and understand the basic knowledge in spectral theory.The article will summarize the basic definitions, properties and theories in the spectral theory to help the readers understand the spectral theory. In the article, I will follow the basic idea from the spectral of the bounded linear operators to the spectral of the unbounded linear operators. It will introduce the definitions, properties and theories of the spectral theory of the bounded linear operator, the compact operator, the normal operator, the self-adjoint operator, the unitary operator and the unbounded linear operator step by step. Besides the theories, I also give some examples in order to understand the spectral theory of linear operator further.