Arbitrary operator as a sum of Hermitian operators

Question

Probaly already asked.

Show that an arbitrary operator $A$ can be written as $A=B+iC$, where $B$ and $C$ are Hermitian.

I think the matrix version is the sum of a symmetric and antisymmetry part, but I have no idea how to do it in the general case.

Answer 1

Hint

$$B=\frac{A+A^*}{2}\;\;\;\;\;C=\frac{A-A^*}{2i}$$