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On Derivations of Operator Algebras with Involution
- Source :
- Demonstratio Mathematica, Vol 47, Iss 4, Pp 784-790 (2014)
- Publication Year :
- 2014
- Publisher :
- De Gruyter, 2014.
-
Abstract
- The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.
- Subjects :
- Discrete mathematics
Pure mathematics
Banach space
Jordan derivation
General Mathematics
lcsh:Mathematics
Semiprime ring
Hilbert space
derivation
lcsh:QA1-939
Operator space
semiprime ring
ring
Linear map
prime ring
standard operator algebra
symbols.namesake
Operator algebra
and phrases ring
Bounded function
Prime ring
symbols
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 23914661 and 04201213
- Volume :
- 47
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Demonstratio Mathematica
- Accession number :
- edsair.doi.dedup.....0a945bf67d773561522b292212d69ed1