1. Jan 26, 2016 #1

   facenian

   

   if subspace A is invariant with respect to a linear operator, is it true that A is invariant with respect to the inverse operator? if not I think threre is a mistake in Wigners paper in "B. Some immediate simplifications" page 13

    

   facenian, Jan 26, 2016
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3. Jan 26, 2016 #2

   facenian

   

   I'm sorry it's my mistake, I didn't read well. At the begining of the paragraph he says that the subspace is invariant under all lorentz transformation then it must be invariant for [itex]D(L^{-1})[/itex] too

    

   facenian, Jan 26, 2016
4. Jan 26, 2016 #3

   A. Neumaier

   

   Science Advisor

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   Yes, if the linear operator is invertible and maps A onto A.

    

   Last edited: Jan 26, 2016

   A. Neumaier, Jan 26, 2016
5. Jan 26, 2016 #4

   Samy_A

   

   Science Advisor

   Homework Helper

   If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.

    

   Samy_A, Jan 26, 2016
6. Jan 26, 2016 #5

   A. Neumaier

   

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   2016 Award

   Indeed. In infinite dimensions you need to assume more. I corrected my statement accordingly.

    

   A. Neumaier, Jan 26, 2016

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