Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem understanding Wigner's 1939 paper

  1. Jan 26, 2016 #1
    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
     
  2. jcsd
  3. Jan 26, 2016 #2
    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
     
  4. Jan 26, 2016 #3

    A. Neumaier

    User Avatar
    Science Advisor
    2016 Award

    Yes, if the linear operator is invertible and maps A onto A.
     
    Last edited: Jan 26, 2016
  5. Jan 26, 2016 #4

    Samy_A

    User Avatar
    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.
     
  6. Jan 26, 2016 #5

    A. Neumaier

    User Avatar
    Science Advisor
    2016 Award

    Indeed. In infinite dimensions you need to assume more. I corrected my statement accordingly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook