Let $X$, $Y$, and $Z$ be normed vector spaces. If $T: X \to Y$ is compact, $A: Z \to X$ is bounded and linear, and $B: Y \to Z$ is bounded and linear, then $T A: Z \to Y$ and $B T: X \to Z$ are compact.
Analysis
Discussion
This theorem says compactness is preserved when a compact operator is composed with bounded linear maps on either side. It is the ideal property of compact operators.
Proof
No proof available for this theorem.
Prerequisites
(0/3 completed)
Prerequisites Graph
Interactive dependency map showing how this theorem builds on foundational concepts