I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum mechanics rigorously? 


Is there any book on the market that you can recommend? Sometimes, I feel it is nice to have a rigorous book at hand when I am doing physics, which is the main reason why I would like to have such a book.


I especially like books that use quite some functional analysis.



Mathematical statistical qm book-recommendation
The two volumes by Bratteli and Robinson.
The book on lattice gases by Simon also has material on quantum statistical mechanics.


