Title

Centralizers And Jordan Derivations For Csl Subalgebras Of Von Neumann Algebras

Keywords

Centralizers; CSL algebras; Jordan derivations; Von neumann algebras

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.

Publication Date

5-14-2013

Publication Title

Journal of Operator Theory

Volume

69

Issue

1

Number of Pages

117-133

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.7900/jot.2010jul19.1870

Socpus ID

84877319982 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84877319982

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