- https://doi.org/10.7153/oam-07-37
A result concerning two-sided centralizers on algebras with involution
- Jan 1, 2013
- Operators and Matrices
- Nejc Širovnik +1 more
Abstract
The purpose of this paper is to prove the following result.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.Let T : A (X) → L (X) be a linear mapping satisfying the relation 3T (AA * A) = T (A)A * A + AT(A * )A + AA * T (A) for all A ∈ A (X).In this case T is of the form T (A) = λ A for all A ∈ A (X), where λ is some fixed complex number.
- # Fixed Complex Number
- # Standard Operator Algebra
- # Adjoint Operation
- # Complex Hilbert Space
- # Complex Space
- # Linear Mapping
- # Complex Number
- # Operator Algebra
- # Standard Operator
- # Mathematics Subject
