Characterization of Lie centralizable mappings on B(X)
Functional Analysis
2025-02-04 v1 Operator Algebras
Abstract
Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a complex number and h:B(X)--> CI is an additive mapping such that h([A,B])=0 for all A,B in B(X) with AB=W.
Keywords
Cite
@article{arxiv.2502.01213,
title = {Characterization of Lie centralizable mappings on B(X)},
author = {Behrooz Fadaee and Hoger Ghahramani and Ayyoub Majidi},
journal= {arXiv preprint arXiv:2502.01213},
year = {2025}
}