Derivations on the algebra of operators in hilbert C*-modules
Abbreviated Journal Title
Acta. Math. Sin.-English Ser.
Derivations; inner derivations; C*-algebras; Hilbert C*-modules; ZERO PRODUCTS; NEST-ALGEBRAS; CSL ALGEBRAS; Mathematics, Applied; Mathematics
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.
Acta Mathematica Sinica-English Series
"Derivations on the algebra of operators in hilbert C*-modules" (2012). Faculty Bibliography 2010s. 2927.