Families of compact operators on Hilbert spaces and fundamental properties

  • Valter Moretti
Part of the UNITEXT book series (UNITEXT)


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

Authors and Affiliations

  • Valter Moretti
    • 1
  1. 1.Department of MathematicsUniversity of TrentoItaly

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