On Generalized Derivations and Centralizers of Operator Algebras with Involution
- Authors: Ali S.1,2, Fošner A.3, Jing W.4
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Affiliations:
- King Abdulaziz University
- Aligarh Muslim University
- University of Primorska
- Fayetteville State University
- Issue: Vol 53, No 1 (2018)
- Pages: 27-33
- Section: Functional Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/228123
- DOI: https://doi.org/10.3103/S1068362318010053
- ID: 228123
Cite item
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.
About the authors
S. Ali
King Abdulaziz University; Aligarh Muslim University
Author for correspondence.
Email: shakir50@rediffmail.com
Saudi Arabia, Jeddah; Aligarh
A. Fošner
University of Primorska
Email: shakir50@rediffmail.com
Slovenia, Koper
W. Jing
Fayetteville State University
Email: shakir50@rediffmail.com
United States, Fayetteville, NC