Title

Derivations On The Algebra Of Operators In Hilbert C*-Modules

Keywords

C*-algebras; Derivations, inner derivations; Hilbert C*-modules

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.

Publication Date

8-1-2012

Publication Title

Acta Mathematica Sinica, English Series

Volume

28

Issue

8

Number of Pages

1615-1622

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10114-012-0172-6

Socpus ID

84864313236 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84864313236

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