While reading [1], I encountered with the concept "Pucci extremal operator" which is defined by: $$M_\Lambda^-(N):=\left(\sum\text{positive eigenvalues of }N\right)+\Lambda\left(\sum\text{negative eigenvalues of }N\right),\text{ and}$$ $$M_\Lambda^+(N):=-M_\Lambda^-(-N),$$ where $N\in\text{Sym}_{n\times n}$ and $\Lambda\geq 1$.

Then the author claims that the problem $$M_\Lambda^-(D^2u)\leq 0\leq M_\Lambda^+(D^2u)$$ in viscosity sense includes all $C^2$ solutions to uniformly elliptic equations of the form $tr(A(x)D^2u)=0$ where $I\leq A(x)\leq\Lambda I$. Since there is no citation on this, it seems this is well-known result in the field, but I am new to this and I want to know about its motivation, history, etc. I did some article search but I could not find a good reference book or paper that introduces the concept of Pucci extremal operator (of course this may be due to my lacking of searching skill). I will appreciate if anyone would explain the concept or give me some good reference on it. Thank you in advance.

[1] *Mooney, Connor*, **A proof of the Krylov-Safonov theorem without localization**, Commun. Partial Differ. Equations 44, No. 8, 681-690 (2019). ZBL1426.35124.