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|Title:||Centralizers and jordan derivations for csl subalgebras of von neumann algebras|
Von neumann algebras
|Source:||Li, P., Han, D., Tang, W.-S. (2013). Centralizers and jordan derivations for csl subalgebras of von neumann algebras. Journal of Operator Theory 69 (1) : 117-133. ScholarBank@NUS Repository. https://doi.org/10.7900/jot.2010jul19.1870|
|Abstract:||We investigate the centralizers and Jordan derivations for com¬mutative subspace lattice algebras in von Neumann algebras. For any CSL subalgebra A of a von Neumann algebra, we prove that a (weak) Jordan centralizer Φ (i.e Φ : A → A is an additive mapping satisfying 2Φ (A2) = Φ(A) A + AΦ(A) for all A ∈ A) is automatically a centralizer. Similarly, we show that every Jordan derivation of A is a derivation. Additionally, we obtain concrete characterizations of centralizers for standard subalgebras of CSL algebras, and a stronger result is also obtained for standard subalgebras of nest algebras. © Theta, 2013.|
|Source Title:||Journal of Operator Theory|
|Appears in Collections:||Staff Publications|
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