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Infinite tensor products of completely positive semigroups

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Abstract.

We construct a new class of semigroups of completely positive maps on \( {\Cal B}(H) \) which can be decomposed into an infinite tensor product of such semigroups. Under suitable hypotheses, the minimal dilations of these semigroups to E 0-semigroups are pure, and have no normal invariant states. Concrete examples are discussed in some detail.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley CA 94720, USA, e-mail: arveson@math.berkeley.edu, , , , , , US

    William Arveson

  2. Department of Mathematics, U. S. Naval Academy, Annapolis MD 21402, USA, e-mail: gip@usna.edu, , , , , , US

    Geoffrey Price

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  1. William Arveson
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  2. Geoffrey Price
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Arveson, W., Price, G. Infinite tensor products of completely positive semigroups. J.evol.equ. 1, 221–242 (2001). https://doi.org/10.1007/PL00001369

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  • DOI: https://doi.org/10.1007/PL00001369

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