Spectral Theory and Quantum Mechanics pp 309-378 | Cite as

# Spectral Theory I: generalities, abstract *C*^{*}-algebras and operators in B(H)

Chapter

## Abstract

In this purely mathematically-flavoured chapter we introduce the basic spectral theory for operators on normed spaces, up to the notion of spectral measure and the spectral decomposition theorem for normal operators in B(H), with H a Hilbert space. (The spectral theorem for *unbounded* self-adjoint operators will be discussed in the next chapter.) Here we present a number of general result in the abstract theory of C^{*}-algebras and ^{*}-homomorphisms.

## Copyright information

© Springer-Verlag Italia 2013