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**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 [tex]\sqrt{A}(H)[/tex] is a closed set

## Homework Equations

## The Attempt at a Solution

Facts that i know that might help..

1)Square root of a symmetric operator is also symmetric

2)[tex]\sqrt{A}(H)[/tex]>=0