CENTRALIZERS AND JORDAN DERIVATIONS FOR CSL SUBALGEBRAS OF VON NEUMANN ALGEBRAS

    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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