Spectral Theory for Bounded Operators on Hilbert Space

Abstract

This thesis is an exposition of spectral theory for bounded operators on Hilbert space. Detailed proofs are given for the functional calculus, the multiplication operator, and the projection-valued measure versions of the spectral theorem for self-adjoint bounded operators. These theorems are then generalized to finite sequences of self-adjoint and commuting bounded operators. Finally, normal bounded operators are discussed, as a particular case of the generalization.