Perturbation of the Wigner equation in inner product C{sup *}-modules

Journal Article · Sat Mar 15 00:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2898486· OSTI ID:21100249

Chmielinski, Jacek ^[1]; Ilisevic, Dijana ^[2]; Moslehian, Mohammad Sal ^[3]; Sadeghi, Ghadir ^[4]

---

1. Institute of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Krakow (Poland)
2. Department of Mathematics, University of Zagreb, Bijenicka 30, P.O. Box 335, 10 002 Zagreb (Croatia)
3. Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashad 91775 (Iran, Islamic Republic of)
4. Banach Mathematical Research Group (BMRG), Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775 (Iran, Islamic Republic of)

Let A be a C*-algebra and B be a von Neumann algebra that both act on a Hilbert space H. Let M and N be inner product modules over A and B, respectively. Under certain assumptions, we show that for each mapping f:M{yields}N satisfying parallel |<f(x),f(y)>|-|<x,y>| parallel {<=}{phi}(x,y) (x,y(set-membership sign)M), where {phi} is a control function, there exists a solution I:M{yields}N of the Wigner equation |<I(x),I(y)>|=|<x,y>| (x,y(set-membership sign)M) such that parallel f(x)-I(x) parallel {<=}{radical}({phi}(x,x)) (x(set-membership sign)M)

• OSTI ID: 21100249
• Journal Information: Journal of Mathematical Physics, Vol. 49, Issue 3; Other Information: DOI: 10.1063/1.2898486; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CONTROL THEORY
EQUATIONS
FUNCTIONS
HILBERT SPACE
MAPPING
MATHEMATICAL SOLUTIONS
PERTURBATION THEORY