Linear Maps Which are Anti-derivable at Zero Abulhamil, Doha Adel Jamjoom, Fatmah B. Peralta Pereira, Antonio Miguel C∗ -algebra Banach bimodule Derivation Anti-derivation Maps ∗ -anti-derivable at zero A.M. Peralta was partially supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and European Regional Development Fund Project No. PGC2018-093332-B-I00, Junta de Andalucia Grant FQM375 and Proyecto de I + D + i del Programa Operativo FEDER Andalucia 2014-2020, ref. A-FQM-242-UGR18. This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University. The authors, therefore, gratefully acknowledge DSR technical and financial support. The results in this paper are part of the first author's PhD thesis at King Abdulaziz University. We acknowledge the thorough revision made by the anonymous referee including several sharp comments on Theorem 6. Let T:A→X be a bounded linear operator, where A is a C∗ -algebra, and X denotes an essential Banach A-bimodule. We prove that the following statements are equivalent: (a): T is anti-derivable at zero (i.e., ab=0 in A implies T(b)a+bT(a)=0 ); (b): There exist an anti-derivation d:A→X∗∗ and an element ξ∈X∗∗ satisfying ξa=aξ, ξ[a,b]=0, T(ab)=bT(a)+T(b)a−bξa, and T(a)=d(a)+ξa, for all a,b∈A . We also prove a similar equivalence when X is replaced with A∗∗ . This provides a complete characterization of those bounded linear maps from A into X or into A∗∗ which are anti-derivable at zero. We also present a complete characterization of those continuous linear operators which are ∗-anti-derivable at zero. 2020-11-11T13:20:18Z 2020-11-11T13:20:18Z 2020-03 info:eu-repo/semantics/article bulhamil, D.A., Jamjoom, F.B. & Peralta, A.M. Linear Maps Which are Anti-derivable at Zero. Bull. Malays. Math. Sci. Soc. 43, 4315–4334 (2020). [https://doi.org/10.1007/s40840-020-00918-7] http://hdl.handle.net/10481/64208 10.1007/s40840-020-00918-7 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Springer Nature