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Stochastics in Finite and Infinite Dimensions pp 89–99Cite as

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A Covariant Quantum Stochastic Dilation Theory

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Abstract

A covariant version of the dilation theory for quantum dynamical semigrops is established, including both Bhat-Parthasarathy type and Evans-Hudson type dilation. It is shown in particular that every uniformly continuous quantum dynamical semigroup on a separable C*-algebra or a von Neumann algebra, which is covariant under a suitable group-action, admits a covariant Evans-Hudson dilation in some appropriate Fock space.

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References

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, Delhi Centre, 7, SJSS Marg, New Delhi, 110016, India

    Partha Sarathi Chakraborty, Debashish Goswami & Kalyan B. Sinha

Authors
  1. Partha Sarathi Chakraborty
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  2. Debashish Goswami
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  3. Kalyan B. Sinha
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Nagoya University, Nagoya, Japan

    Takeyuki Hida

  2. Indian Statistical Institute, New Delhi, 110016, India

    Rajeeva L. Karandikar

  3. Department of Applied Sciences, Kyushu University, Kyushu, Japan

    Hiroshi Kunita

  4. Department of Mathematics, University of Tennessee, Knoxville, TN, 47996, USA

    Balram S. Rajput

  5. Department of Mathematics, Kyoto University, Kyoto, Japan

    Shinzo Watanabe

  6. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    Jie Xiong

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© 2001 Springer Science+Business Media New York

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Chakraborty, P.S., Goswami, D., Sinha, K.B. (2001). A Covariant Quantum Stochastic Dilation Theory. In: Hida, T., Karandikar, R.L., Kunita, H., Rajput, B.S., Watanabe, S., Xiong, J. (eds) Stochastics in Finite and Infinite Dimensions. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0167-0_5

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  • DOI: https://doi.org/10.1007/978-1-4612-0167-0_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6643-3

  • Online ISBN: 978-1-4612-0167-0

  • eBook Packages: Springer Book Archive

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