Quantum stochastic processes for maps on Hilbert C*-modules
- Authors
- Heo, Jaeseong; Ji, Un Cig
- Issue Date
- May-2011
- Publisher
- AMER INST PHYSICS
- Citation
- JOURNAL OF MATHEMATICAL PHYSICS, v.52, no.5
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL PHYSICS
- Volume
- 52
- Number
- 5
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/168552
- DOI
- 10.1063/1.3582778
- ISSN
- 0022-2488
- Abstract
- We discuss pairs (phi, Phi) of maps, where phi is a map between C*-algebras and Phi is a phi-module map between Hilbert C*-modules, which are generalization of representations of Hilbert C*-modules. A covariant version of Stinespring's theorem for such a pair (phi, Phi) is established, and quantum stochastic processes constructed from pairs ({phi(t)}, {Phi(t)}) of families of such maps are studied. We prove that the quantum stochastic process J = {J(t)} constructed from a phi-quantum dynamical semigroup Phi = {Phi(t)} is a j-map for the quantum stochastic process j = {j(t)} constructed from the given quantum dynamical semigroup phi = {phi(t)}, and that J is covariant if the phi-quantum dynamical semigroup Phi is covariant.
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