@misc{10481/64208,
year = {2020},
month = {3},
url = {http://hdl.handle.net/10481/64208},
abstract = {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.},
organization = {Spanish Ministry of Science, Innovation and Universities (MICINN)},
organization = {European Regional Development Fund Project 	
PGC2018-093332-B-I00},
organization = {Junta de Andalucia
	
FQM375},
organization = {Proyecto de I + D + i del Programa Operativo FEDER Andalucia 2014-2020 	
A-FQM-242-UGR18},
organization = {Deanship of Scientific Research (DSR), King Abdulaziz University},
organization = {DSR},
publisher = {Springer Nature},
keywords = {C∗ -algebra},
keywords = {Banach bimodule},
keywords = {Derivation},
keywords = {Anti-derivation},
keywords = {Maps ∗ -anti-derivable at zero},
title = {Linear Maps Which are Anti-derivable at Zero},
doi = {10.1007/s40840-020-00918-7},
author = {Abulhamil, Doha Adel and Jamjoom, Fatmah B. and Peralta Pereira, Antonio Miguel},
}