Hi!!!

I don't know how to solve this.

Let $\displaystyle V$ a inner product space, $\displaystyle T: V \rightarrow V$ a linear aplication and $\displaystyle T^*$ its adjoint.

Prove that $\displaystyle ker(TT^*+T^*T) = ker(T)\cap ker(T^*)$

Obviously there is an easy inclusion

Thanks!!

Everk