TITLE: The classical Krein-Rutman theorem
QUESTION [8 upvotes]: The classical Krein-Rutman theorem states that any positive compact linear endomorphism $T:X \to X$ on a Banach space $X$ with positive spectral radius $r(T)$ has an eigenvalue $r(T)$ with a positive eigenvector. Papers and textbooks seem to write off the theorem as "standard" and "well-known", but I have not been able to locate any exposition with a proof of the theorem.
Is there a reference (preferably a textbook) including the statement and the proof of the theorem? (The original paper of Krein and Rutman appears to be in Russian, which I cannot read.)

REPLY [6 votes]: For Banach lattices, a statement and a sketch of the proof can be found in Abramovich and Aliprantis's article "Positive operators" in the Handbook of the Geometry of Banach Spaces: see Google books excerpt