# Problem understanding Wigner's 1939 paper

1. Jan 26, 2016

### 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

2. Jan 26, 2016

### 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 $D(L^{-1})$ too

3. Jan 26, 2016

### A. Neumaier

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

Last edited: Jan 26, 2016
4. Jan 26, 2016

### Samy_A

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

5. Jan 26, 2016

### A. Neumaier

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