12- https://doi.org/10.1007/s10474-006-0071-3
On derivations of algebras with involution
- Sep 1, 2006
- Acta Mathematica Hungarica
- Joso Vukman
Abstract
Let X be a complex Hilbert space, let L(X) be the 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 D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras.
- # Standard Operator Algebra
- # Derivations Of Algebras
- # Adjoint Operation
- # Complex Hilbert Space
- # Linear Mapping
- # Complex Space
- # Operator Algebra
- # Standard Operator
- # Linear Operators
