Definition:Invariant Subspace

Definition

Let $H$ be a Hilbert space.

Let $A \in B \left({H}\right)$ be a bounded linear operator.

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

Then $M$ is said to be an invariant subspace for $A$ iff $h \in M \implies Ah \in M$.

That is, if $AM \subseteq M$.

Also see

• Reducing Subspace

Sources

• 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.3.5$