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

  1. Jul 18, 2012 #1
    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.
     
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  3. Jul 18, 2012 #2

    mfb

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    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.
     
  4. Jul 18, 2012 #3
    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?
     
  5. Jul 18, 2012 #4

    mfb

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    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".
     
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