Derivations on the algebra of operators in hilbert C*-modules

    Authors

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

    Comments

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    Abbreviated Journal Title

    Acta. Math. Sin.-English Ser.

    Keywords

    Derivations; inner derivations; C*-algebras; Hilbert C*-modules; ZERO PRODUCTS; NEST-ALGEBRAS; CSL ALGEBRAS; Mathematics, Applied; Mathematics

    Abstract

    Let M be a full Hilbert C*-module over a C*-algebra A, and let End* (A) (M) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End* (A) (M) is an inner derivation, and that if A is sigma-unital and commutative, then innerness of derivations on "compact" operators completely decides innerness of derivations on End* (A) (M). If A is unital (no commutativity is assumed) such that every derivation of A is inner, then it is proved that every derivation of End*A(L (n) (A)) is also inner, where L (n) (A) denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist x (0), y (0) a M such that < x (0), y (0) > = 1, we characterize the linear A-module homomorphisms on End* (A) (M) which behave like derivations when acting on zero products.

    Journal Title

    Acta Mathematica Sinica-English Series

    Volume

    28

    Issue/Number

    8

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1615

    Last Page

    1622

    WOS Identifier

    WOS:000306172700009

    ISSN

    1439-8516

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