Maps preserving fixed points of generalized product of operators

Jordan product and fixed points preservers

“…for all A, B ∈ B(X), where X is a complex Banach space with dim X ≥ 3, they proved that there exists a nonzero scalar α ∈ C with α 3 = 1 such that φ(A) = αA for every A ∈ B(X). In [2] Y. Bouramdane et al proved the previous result for the generalized product of operators.…”

“…This paper is motivated by the ideas from [2], but the proofs of our main results require new agruments. The statements of our main result can be stated as follows.…”