# On a proof that a set of operators with a specific property is closed under addition

1. Jul 18, 2012

### Crot

Could you please give me a hint on how to show that a set of operators with a property P is closed under addition? In other words, how one could prove that a sum of any two operators from the set still possesses this property P. The set is assumed to be infinite.

Any references, comments, suggestions, etc. will be kindly appreciated.

2. Jul 18, 2012

### Staff: Mentor

Re: On a proof that a set of operators with a specific property is closed under addit

It depends on the set of operators and on P.

One general concept: Take an arbitrary sum of two operators, show that the sum is an operator which satisfies P.

3. Jul 18, 2012

### Crot

Re: On a proof that a set of operators with a specific property is closed under addit

Thank you for your answer. But, this concept is really too general.
Are there any other techniques?

4. Jul 18, 2012

### Staff: Mentor

Re: On a proof that a set of operators with a specific property is closed under addit

Your question is extremely general. Just one step more general would be "how do you prove a mathematical statement".

All techniques are some sort of this proof, as it is the definition of "closed".