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Conservative dilations of dissipative multidimensional systems: The commutative and non-commutative settings

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Abstract

We establish the existence of conservative dilations for various types of dissipative non-commutative N-dimensional (N-D) systems. As a corollary, a criterion of existence of conservative dilations for corresponding dissipative commutative N-D systems is obtained. We point out the cases where this criterion is always fulfilled, and the cases where it is not always fulfilled.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. Department of Mathematics, Drexel University, 3141 Chestnut Str., Philadelphia, PA, 19104, USA

    Dmitry S. Kaliuzhnyi-Verbovetskyi

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  1. Joseph A. Ball
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  2. Dmitry S. Kaliuzhnyi-Verbovetskyi
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Correspondence to Dmitry S. Kaliuzhnyi-Verbovetskyi.

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Ball, J.A., Kaliuzhnyi-Verbovetskyi, D.S. Conservative dilations of dissipative multidimensional systems: The commutative and non-commutative settings. Multidim Syst Sign Process 19, 79–122 (2008). https://doi.org/10.1007/s11045-007-0025-0

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