Exercise 7.C.5

Answers

Proof. Suppose $S, T \in L (V)$ are positive operators. Then

{(S + T)}^{∗} = S^{∗} + T^{∗} = S + T .

Hence $S + T$ is self-adjoint. Moreover, for all $v \in V$ , we have

⟨ (S + T) v, v ⟩ = ⟨ Sv, v ⟩ + ⟨ Tv, v ⟩ \geq 0,

showing that $S + T$ is positive. □

celiopassos

2017-10-06 00:00