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Apr 10, 2012 at 21:30 comment added Matthias Ludewig In Kato's book "Perturbation theory of linear operators" is a chapter on semiboundedness (in 1995th edition, it starts p310). Also, if you know german, you find the exact theorem in "Dirk Werner: Funktionalanalysis". There it is Theorem VII.2.11. Kato's book, by the way, is a standard reference and you will find everything there what I claimed in my post.
Apr 10, 2012 at 7:54 comment added Per Alexandersson How about looking at the references in en.wikipedia.org/wiki/Self-adjoint_operator
Apr 9, 2012 at 16:01 history answered Matthias Ludewig CC BY-SA 3.0