Definition:Invariant Subspace of Normed Vector Space
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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 (with respect to $T$).
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.3$: The normed space $\map {CL} {X,Y}$. Operator norm and the normed space $\map {CL} {X, Y}$