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Positivity

, Volume 22, Issue 1, pp 27–37 | Cite as

Structure theorem of the generator of a norm continuous completely positive semigroup: an alternative proof using Bures distance

  • Mithun Mukherjee
Article

Abstract

Here we present an alternative proof using Bures distance that the generator L of a norm continuous completely positive semigroup acting on a \(C^*\)-algebra \({\mathcal {B}}\subset \mathcal B(H)\) has the form \( L(b) = \Psi (b) + k^*b+bk\), \(b\in {\mathcal {B}}\) for some completely positive map \(\Psi :{\mathcal {B}}\rightarrow {\mathcal {B}}(H)\) and \(k\in {\mathcal {B}}(H)\).

Keywords

\(C^*\)-algebras Von Neumann algebras Quantum dynamical semigroups Bures distance 

Mathematics Subject Classification

46L57 46L55 46L08 

Notes

Acknowledgements

I thank B.V. Rajarama Bhat for several useful discussions on the subject. I also thank DST-Inspire (IFA-13 MA-20) for financial support.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.School of MathematicsIndian Institute of Science Education and Research ThiruvananthapuramThiruvananthapuramIndia

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