Acta Applicandae Mathematica

, Volume 32, Issue 1, pp 89–98 | Cite as

Cyclic vectors for Hilbert algebras

  • Xiu-Chi Quan


In this paper, we give a simple proof of the Stone-von Neumann theorem about the irreducible unitary representations of Heisenberg groups. First of all, we prove a result about the representations of Hilbert algebras of Hilbert-Schmidt operators on a Hilbert space. Then we use it to give a simple proof of the Stone-von Neumann theorem. Applications to theoretical physics are mentioned.

Mathematics subject classifications (1991)

22D30 46L89 

Key words

Hilbert algebra representation Stone-von Neumann theorem 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Xiu-Chi Quan
    • 1
  1. 1.Institute of Fundamental TheoryUniversity of FloridaGainesvillUSA

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