Spectral Theory and Quantum Mechanics pp 161-207 | Cite as

# Families of compact operators on Hilbert spaces and fundamental properties

Chapter

## Abstract

The aim of this chapter, from the point of view of QM applications, is to introduce certain types of operators used to define *quantum states*. These operators, known in the literature as *operators of trace class*, *or nuclear operators*, are bounded operators on a Hilbert space that admit a trace. In order to introduce them it is necessary to define first *compact operators*, also known as *completely continuous* operators, that play an important role in several branches of mathematics and physical applications independent of quantum theories.

## Copyright information

© Springer-Verlag Italia 2013