MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS
- Title
- MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS
- Author
- 박춘길
- Keywords
- Skew Lie product; factor von Neumann algebras; preserver problems
- Issue Date
- 2012-03
- Publisher
- ELSEVIER SCIENCE B.V. AMSTERDAM
- Citation
- Acta Mathematica Scientia, 2012, 32(2), P.531-538
- Abstract
- Let A be a factor von Neumann algebra and Phi be a nonlinear surjective map from A onto itself. We prove that, if Phi satisfies that Phi(A)Phi(B) - Phi(B)Phi(A)* = AB - BA* for all A, B is an element of A, then there exist a linear bijective map Psi: A -> A satisfying Psi(A)Psi(B) - Psi(B)Psi(A)* = AB - BA* for A, B is an element of A and a real functional h on A with h(0) = 0 such that Phi(A) = Psi(A) + h(A)I for every A is an element of A. In particular, if A is a type I factor, then, Phi(A) = cA + h(A)I for every A is an element of A, where c = +/- 1.
- URI
- https://www.sciencedirect.com/science/article/pii/S0252960212600356?via%3Dihubhttps://repository.hanyang.ac.kr/handle/20.500.11754/72994
- ISSN
- 0252-9602
- DOI
- 10.1016/S0252-9602(12)60035-6
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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