I am looking for a second proof of Jordan-Von Neumann theorem that characterizes inner product in normed spaces. The book "Inner Product Structures: Theory and Applications" talks about a second proof based in Frechet condition.


I would thank anyone who can help me to know how is exactly the second demonstration, the pages that talk about the second proof are hidden (is a book preview) and I cannot find such proof searching in google.


Book (Preview), the theorem proof starts at 114:


[Preview of book in question](http://books.google.es/books?id=nBWsDtVfsbsC&printsec=frontcover&hl=es&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)
Regards, Joaquín.



Second proof of Jordan-Von Neumann theorem
The second proof is from
B. Reznick, Banach spaces which satisfy linear identities. Pacif. J. Math. 74, 221-233.


