On Generalized Derivations and Centralizers of Operator Algebras with Involution
Document Type
Article
Publication Date
1-1-2018
Abstract
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and A(H) ? B(H) be a standard operator algebra which is closed under the adjoint operation. Let F: A(H)? B(H) be a linear mapping satisfying F(AA*A) = F(A)A*A + Ad(A*)A + AA*d(A) for all A ? A(H), where the associated linear mapping d: A(H) ? B(H) satisfies the relation d(AA*A) = d(A)A*A + Ad(A*)A + AA*d(A) for all A ? A(H). Then F is of the form F(A) = SA ? AT for all A ? A(H) and some S, T ? B(H), that is, F is a generalized derivation. We also prove some results concerning centralizers on A(H) and semisimple H*-algebras.
Recommended Citation
Ali, S.; Fošner, A.; and Jing, W., "On Generalized Derivations and Centralizers of Operator Algebras with Involution" (2018). College of Health, Science, and Technology. 908.
https://digitalcommons.uncfsu.edu/college_health_science_technology/908