How to prove the closedness of \sqrt{A}(H)?

  • Thread starter Thread starter Mechmathian
  • Start date Start date
  • Tags Tags
    Important
Mechmathian
Messages
35
Reaction score
0
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


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
 
Physics news on Phys.org
Is there another section that I should ask about the homework problems I have? I don't think anyone of them was yet answered?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

How should I find the nontrivial stationary paths?
Replies
10
Views
2K
Prove that the integral is equal to ##\pi^2/8##
2
Replies
96
Views
4K
Bounded operators on Hilbert spaces
Replies
43
Views
4K
Showing that f(x,y) = √|xy| is not differentiable at (0,0)
Replies
9
Views
5K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
Replies
2
Views
2K
Finding domain for when composite function is continuous
Replies
3
Views
1K
If H is a subgroup, then H is subgroup of normalizer
Replies
5
Views
2K
Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
529
Differentiability in higher dimensions
Replies
11
Views
2K
Using a Taylor expansion to prove equality
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top