@misc{10481/69652,
year = {2020},
month = {9},
url = {http://hdl.handle.net/10481/69652},
abstract = {A linear mapping T on a JB∗-triple is called triple derivable at orthogonal pairs if for every a,b,c∈E with a⊥b we have
0={T(a),b,c}+{a,T(b),c}+{a,b,T(c)}.
We prove that for each bounded linear mapping T on a JB∗-algebra A the following assertions are equivalent:
(a) T is triple derivable at zero;
(b) T is triple derivable at orthogonal elements;
(c) There exists a Jordan ∗-derivation D:A→A∗∗, a central element ξ∈A∗∗sa, and an anti-symmetric element η in the multiplier algebra of A, such that
T(a)=D(a)+ξ∘a+η∘a, for all a∈A;

(d) There exist a triple derivation δ:A→A∗∗ and a symmetric element S in the centroid of A∗∗ such that T=δ+S.
The result is new even in the case of C∗-algebras. We next establish a new characterization of those linear maps on a JBW∗-triple which are triple derivations in terms of a good local behavior on Peirce 2-subspaces. We also prove that assuming some extra conditions on a JBW∗-triple M, the following statements are equivalent for each bounded linear mapping T on M:
(a) T is triple derivable at orthogonal pairs;
(b) There exists a triple derivation δ:M→M and an operator S in the centroid of M such that T=δ+S. \end{enumerate}},
organization = {Higher Education and Scientific Research Ministry in Tunisia
	UR11ES52},
organization = {Spanish Ministry of Science, Innovation and Universities (MICINN)},
organization = {European Commission
	PGC2018-093332-B-I00},
organization = {Programa Operativo FEDER 2014-2020},
organization = {Junta de Andalucía
	A-FQM-242-UGR18	
	FQM375},
publisher = {Springer Nature},
title = {A linear preserver problem on maps which are triple derivable at orthogonal pairs},
doi = {10.1007/s13398-021-01082-8},
author = {Essaleh, Ahlem Ben Ali and Peralta Pereira, Antonio Miguel},
}