Exercise 17, § 6

Tag 02FK, permanent. Cite it as [Bourbaki, Tag 02FK].

Spectral Theories, I, p. 182

Let $A$ be a star algebra and $x\in A$ . If $x=a-b$ with $a, b$ positive and $ab=ba= 0$ , then $a=x^+$ and $b=x^-$ .