what is the name of this book by Rudin?

Question

Product and sum of positive operators is positive

in this question OP states that :

There is a theorem in Rudin (12.32) that says that for every $T\in B(H)$ we have an equivalence: $T$ is positive $\Leftrightarrow$ $T$ is self adjoint, i.e.$T=T^*$ and $\sigma(T)\subset [0,\infty)$.

I checked "principles of mathematical analysis" and it has got just 11 sections so I guess it's not the book which OP was referring to.

I'd like to know which is it and if possible other books where this same theorem is proven.

thanks !

Answer 1

That book is Functional Analysis, published by McGraw-Hill.