If we are working in a complex inner product space with elements f,g then is $\langle f,g \rangle = \overline{\langle g,f \rangle} = \langle \overline{g},\overline{f} \rangle$ ? Obviously the first equality is true but I am wondering if the complex conjugate can be brought into the inner product.
We can assume that $\overline{f}$ is defined. In the specific problem I am working on we are in a reproducing kernel Hilbert space.
TY!