Spectral Analysis, a General Approach in Normed Spaces
Fabio Botelho · 2020
This chapter presents some results about the spectrum and resolvent sets for a bounded operator defined on a normed space. It discusses sesquilinear functionals and shows the results of the functionals in the Hilbert space. The chapter describes the spectrum of a linear operator defined on a Banach space and the spectral theorem for bounded self-adjoint operators. It explains the spectral theorem and the spectral decomposition of unitary transformations in a Hilbert space, and proves that every unitary transformation has a spectral decomposition. The chapter introduces unbounded operators and symmetric and self-adjoint operators. It also proves the spectral theorem using Cayley transform.