# Very important

1. Apr 29, 2008

### Mechmathian

Very important!!

1. The problem statement, all variables and given/known data
If A is an symmetric operator in separable hilbert space (H) and
1)A>=0 (which means that (Ax, x)>=0 for any x)
2)A(H) is a closed set

How do you proove that $$\sqrt{A}(H)$$ is a closed set

2. Relevant equations

3. The attempt at a solution
Facts that i know that might help..
1)Square root of a symmetric operator is also symmetric
2)$$\sqrt{A}(H)$$>=0

2. Apr 30, 2008

### Mechmathian

Is there another section that I should ask about the hw problems I have? I don't think any one of them was yet answered?