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Quantum stochastic processes for maps on Hilbert C*-modules

Title
Quantum stochastic processes for maps on Hilbert C*-modules
Author
허재성
Keywords
Hilbert space; Stochastic processes; Algebras; Subspaces; Noncommutative field theory
Issue Date
2011-05
Publisher
AMER INST PHYSICS, 1305 WALT WHITMAN RD, STE 300, MELVILLE, NY 11747-4501 USA
Citation
JOURNAL OF MATHEMATICAL PHYSICS; MAY 2011, 52 5, 16p.
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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3582778]
URI
http://aip.scitation.org/doi/abs/10.1063/1.3582778http://hdl.handle.net/20.500.11754/36334
ISSN
0022-2488
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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