Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $T : H\rightarrow H$ be a continuous, injective, symmetric operator on a real Hilbert space $H$. Let $V$ be a subspace of $H$ such that $T(V)$ is dense in $H$. Must $V$ be dense in $H$?

share|improve this question
    
The example you accepted is neither injective nor symmetric. –  Martin Feb 12 '13 at 7:57
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.