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|Title:||Derivations on the algebra of operators in hilbert C*-modules|
Derivations, inner derivations
|Citation:||Li, P.T., Han, D.G., Tang, W.S. (2012-08). Derivations on the algebra of operators in hilbert C*-modules. Acta Mathematica Sinica, English Series 28 (8) : 1615-1622. ScholarBank@NUS Repository. https://doi.org/10.1007/s10114-012-0172-6|
|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 σ-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 ∈ 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. © 2012 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.|
|Source Title:||Acta Mathematica Sinica, English Series|
|Appears in Collections:||Staff Publications|
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