The domain algebra of a CP semigroup
| dc.creator | Arveson, William | |
| dc.date | 2000-05-24 | |
| dc.date.accessioned | 2026-07-25T22:47:01Z | |
| dc.description | A CP semigroup is a semigroup of normal unit-preserving completely positive maps acting on the algebra B(H) of all operators on a separable Hilbert space H. Such a semigroup has a natural generator L; since the individual maps of the semigroup need not be multiplicative, the domain Dom(L) of L is typically an operator system, but not an algebra. However, we show that the set of all operators A in Dom(L), with the property that both A*A and AA* belong to Dom(L), is a *-algebra, called the domain algebra of the CP semigroup. Using this algebra, it is possible to draw a very close parallel with the Laplacian of a Riemannian manifold. We discuss properties of the "symbol" of L as the noncommutative counterpart of a (semidefinite) Riemannian metric, and give examples for which the domain algebra is, and is not, strongly dense in B(H). | |
| dc.description | 19 pages typeset | |
| dc.identifier | https://arxiv.org/abs/math/0005251 | |
| dc.identifier | http://arxiv.org/abs/math/0005251 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/92459 | |
| dc.subject | Operator Algebras | |
| dc.title | The domain algebra of a CP semigroup | |
| dc.type | text |