Definition:Invariant Subspace
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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
Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.3.5$