Antilinear Operator

An antilinear Operator satisfies the following two properties:

$\displaystyle \tilde A [f_1(x)+f_2(x)]$	$\textstyle =$	$\displaystyle \tilde A f_1(x)+\tilde A f_2(x)$
$\displaystyle \tilde A cf(x)$	$\textstyle =$	$\displaystyle c^* \tilde A f(x),$

where