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

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In summary, "very important" is a subjective term that can mean different things to different people. The importance of something can be determined by its impact, value, or relevance, as well as factors such as consequences, resources, and personal needs and desires. Prioritizing tasks or goals is important in order to make efficient use of time and resources and prevent important things from being overlooked. Determining what is most important is a personal process that involves self-reflection, identifying values and goals, and seeking input from others or guidance from a mentor or counselor.
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Mechmathian
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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
 
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Is there another section that I should ask about the homework problems I have? I don't think anyone of them was yet answered?
 

What is the definition of "very important"?

"Very important" is a subjective term that can mean different things to different people. Generally, it refers to something that is crucial, significant, or essential.

How is the importance of something determined?

The importance of something can be determined by its impact, value, or relevance. Factors such as the consequences of not having it, the amount of resources required to obtain it, and the level of need or desire for it can also contribute to its perceived importance.

Can something be considered "very important" to one person but not to another?

Yes, as mentioned before, the term "very important" is subjective. What may be crucial to one person may not be as significant to another. Each individual's experiences, beliefs, and priorities can influence how they perceive the importance of something.

Why is it important to prioritize tasks or goals?

Prioritizing tasks or goals allows individuals to focus on what is most important or urgent, thus making the most efficient use of their time and resources. It can also help prevent important things from being overlooked or forgotten.

How can someone determine what is most important to them?

Determining what is most important to someone is a personal process. It involves self-reflection, identifying one's values and goals, and considering the potential impact or consequences of different things. It may also involve seeking input from others or seeking guidance from a mentor or counselor.

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