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Infinite tensor products of completely positive semigroups |
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| Authors: | William Arveson Geoffrey Price |
| Affiliation: | (1) Department of Mathematics, University of California, Berkeley CA 94720, USA, e-mail: arveson@math.berkeley.edu, US;(2) Department of Mathematics, U. S. Naval Academy, Annapolis MD 21402, USA, e-mail: gip@usna.edu, US |
| Abstract: | We construct a new class of semigroups of completely positive maps on 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. |
| Keywords: | and phrases: Completely positive semigroup minimal dilation pure E0-semigroup absorbing state invariant normal state. |
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