Does this binary operation have a name?

Question

Does the following binary operator on abstract linear maps $A,B:\mathbb{C}^N \rightarrow \mathbb{C}^N$, have a name:

$[\{A,B\}]:= AB^{\dagger} - BA^{\dagger}$

clearly, it is real bi-linear, but not complex bi-linear. It is also anti-symmetric.