Do Hilbert Space Isomorphism Map Dense Sets to Dense Sets?

Suppose that H, K are Hilbert spaces, and A : H -> K is a bounded linear operator and an isomorphism.



If X is a dense set in H, then is A(X) a dense set in K?



Any references to texts would also be helpful.

via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=713660&goto=newpost