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Very important

  • #1
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
 

Answers and Replies

  • #2
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?
 

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