# Very important

Very important!!

## Homework Statement

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

## 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