# Quantum systems and representation theorem

Quantum systems and representation theorem In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum $$L^{\infty }$$ -system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Quantum systems and representation theorem

, Volume 17 (3) – Oct 26, 2012
21 pages

/lp/springer_journal/quantum-systems-and-representation-theorem-TlmwloHaS1
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0208-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum $$L^{\infty }$$ -system.

### Journal

PositivitySpringer Journals

Published: Oct 26, 2012

### References

• Quantum duality, unbounded operators and inductive limits
Dosi, AA

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