Problem understanding Wigner's 1939 paper

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  • #1
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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
 

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  • #2
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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
 
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A. Neumaier
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if subspace A is invariant with respect to a linear operator, is it true that A is invariant with respect to the inverse operator?
Yes, if the linear operator is invertible and maps A onto A.
 
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  • #4
Samy_A
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Yes, if the linear operator is invertible (and hence maps A onto A).
If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.
 
  • #5
A. Neumaier
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If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.
Indeed. In infinite dimensions you need to assume more. I corrected my statement accordingly.
 

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