Definition:Invariant Subspace of Normed Vector Space

Definition
Let $\struct {X, \norm {\, \cdot \,}_X}$ be a normed vector space.

Let $Y \subseteq X$ be a subspace of $X$.

Let $T : X \to X$ be a linear operator such that $T Y \subseteq Y$.

Then $Y$ is called the invariant subspace ( $T$).