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Feb 11, 2010 at 17:19 comment added Bill Johnson It is also in many Real Analysis textbooks. See, e.g., problem 22 after section 5.2 in Folland's Real Analysis, 2nd ed.
Feb 11, 2010 at 3:49 comment added Yemon Choi Just to add that Bill's answer for general Banach spaces can probably be found in several functional analysis textbooks, but can definitely be found in Chapter 4 of Rudin's FA. (Thm 4.14 in my copy, 2nd ed)
Feb 11, 2010 at 2:39 comment added Tom LaGatta Simple, as I thought. Thanks, Ady!
Feb 11, 2010 at 2:28 comment added Ady A linear subspace of a Hilbert space is dense iff its orthogonal is {0}...
Feb 11, 2010 at 2:21 vote accept Tom LaGatta
Feb 11, 2010 at 2:18 comment added Tom LaGatta Bill, thanks so much for the response. That answers my question; could you please give me an argument or a citation so I could look it up?
Feb 11, 2010 at 2:11 history answered Bill Johnson CC BY-SA 2.5