Definition:Invariant Subspace

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Let $H$ be a Hilbert space.

Let $A \in \map B H$ be a bounded linear operator.

Let $M$ be a closed linear subspace of $H$.

Then $M$ is said to be an invariant subspace for $A$ if and only if $h \in M \implies A h \in M$.

That is, if and only if $AM \subseteq M$.

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