Thursday, October 16, 2008
I am looking for an elementary proof of the fact that an unbounded operator cannot have the whole Hilbert space as its domain of definition. In the textbooks I had a look at this follows from the closed graph theorem which then is proved using somewhat heavy functional analysis machinery. What I am looking for is something that is accessible to physicists that have just learned about unbounded operators and that could be turned into a homework problem. If you know such a reference or could give me a hint (in the comments or to email@example.com) I would greatly appreciate it!
Posted by Robert at 10:40 AM