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

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.