- #1
Mechmathian
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Very important!
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
Facts that i know that might help..
1)Square root of a symmetric operator is also symmetric
2)\sqrt{A}(H)>=0
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
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)\sqrt{A}(H)>=0
