#### Title

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

#### 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

#### ISSN

1439-8516

#### Recommended Citation

"Derivations on the algebra of operators in hilbert C*-modules" (2012). *Faculty Bibliography 2010s*. 2927.

https://stars.library.ucf.edu/facultybib2010/2927

## Comments

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