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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.

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- #1

- 107

- 0

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.

- #2

- 82

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It is true. Suppose, that A(X) is not dense. Then let V be a non-empty open set in K \ A(X). The pullback of V by A is open (A is bounded) and not empty (A is isomorphism), and by definition it is not in X, which contradicts the fact, that X is dense in H.

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