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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
Yes, if the linear operator is invertible and maps A onto A.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 invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.Yes, if the linear operator is invertible (and hence maps A onto A).
Indeed. In infinite dimensions you need to assume more. I corrected my statement accordingly.If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.