Title

CENTRALIZERS AND JORDAN DERIVATIONS FOR CSL SUBALGEBRAS OF VON NEUMANN ALGEBRAS

Authors

Authors

P. T. Li; D. G. Han;W. S. Tang

Comments

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Abbreviated Journal Title

Appl. Phys. Lett.

Keywords

Centralizers; Jordan derivations; CSL algebras; von Neumann algebras; STANDARD OPERATOR-ALGEBRAS; VONNEUMANN-ALGEBRAS; COMMUTANTS MODULO; NEST-SUBALGEBRAS; LATTICES; RINGS; LIE; Mathematics

Abstract

We investigate the centralizers and Jordan derivations for commutative subspace lattice algebras in von Neumann algebras. For any CSL subalgebra A of a von Neumann algebra, we prove that a (weak) Jordan centralizer Phi (i.e Phi : A -> A is an additive mapping satisfying 2 Phi(A(2)) Phi(A)A + A Phi(A) for all A is an element of 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.

Journal Title

Journal of Operator Theory

Volume

J. Operat. Theor.

Issue/Number

1

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

117

Last Page

133

WOS Identifier

69

ISSN

0379-4024

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