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- Title
Nonlinear commutativity preserving maps on self-adjoint operators.
- Authors
MOLÁNAR, LAJOS; ŭEMRL, PETER
- Abstract
We characterize the bijective nonlinear maps of the set of all self-adjoint bounded linear operators on a complex separable Hilbert space H of dimension at least 3 which preserve commutativity in both directions. Roughly speaking, a bijective map has this property if, and only if, up to a unitary or antiunitary transformation of H, it leaves fixed the self-adjoint parts of the commutative von Neumann algebras on H.
- Subjects
MAPS; NONLINEAR systems; HILBERT space; COMMUTATIVE law (Mathematics); VON Neumann algebras
- Publication
Quarterly Journal of Mathematics, 2005, Vol 56, Issue 4, p589
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hah058