Non-linear analysis 1) I am looking for a book which would give the proof of the following theorem(see below). I didn't find any book who does it:


*

*in infinite dimension (in Rockafellar Convex analysis book we are in finite dimension)

*considering the linear continuous application (written A or L in the following print screen) (I found for example the Fenchel duality theorem but doing it just with the sum, without considering the linear application. I have no ideas of the technical complexity of considering A.)


I know all the theorems I posted are intimately related so if I can find the proof of one of them it could be sufficient to prove the others.
2) More generally i would like to find a book who give the proofs of the pdf: https://www.ljll.math.upmc.fr/mathmodel/enseignement/polycopies/M2B003-AB.pdf
(so in the case the more general).
Thanks for your help!!



The best result of the form you want are in "Convex Analysis in General Vector Spaces" by C Zalinescu 
see also http://www.worldscientific.com/worldscibooks/10.1142/5021
