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## Main Question or Discussion Point

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.

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.