Additive derivations of certain reflexive algebras

    Authors

    P. T. Li; J. P. Ma;J. Wu

    Comments

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    Abbreviated Journal Title

    Houst. J. Math.

    Keywords

    additive derivations; quasi-spatiality; reflexive algebras; J-subspace; lattices; PENTAGON SUBSPACE LATTICES; STANDARD OPERATOR-ALGEBRAS; NEST-ALGEBRAS; ISOMORPHISMS; Mathematics

    Abstract

    Let L be a T-subspace lattice on a Banach space X, AlgL be the associated reflexive algebra and A be a subalgebra of AlgL containing all finite rank operators in AlgL. If either dimK = infinity or dimK(-)(perpendicular to) = infinity for every K is an element of L with K not equal (0) and K- not equal X, then every additive derivation D from A into AlgL is linear and quasi-spatial, that is, there exists a densely defined, closed linear operator T : Dom(T) subset of X -- > X with its domain Dom(T) invariant under every element of A, such that D(A)x = (TA - AT)x for all A is an element of A and X is an element of Dom(T). This result can apply to those reflexive algebras with atomic Boolean subspace lattices and pentagon subspace lattices, respectively.

    Journal Title

    Houston Journal of Mathematics

    Volume

    32

    Issue/Number

    2

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    521

    Last Page

    530

    WOS Identifier

    WOS:000237798100014

    ISSN

    0362-1588

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