@MichaelAlbanese, it would take me pages to introduce all the notations used in the statements. Moreover, the functional spaces are not the most usual, so I think that it is better to check directly in the book.

@AlexM. the theorem does answer the question, you just have to check what means every notation used in the statement (which is not straight forward at all). However, I agree with the fact that there is no way to check the details of the proofs or to rewrite it by yourself.