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A. Neumaier

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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?

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Samy_A

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

- #5

A. Neumaier

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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.

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