Voiculescu's theorem

Voiculescu's theorem is a result in operator theory that states approximate unitary equivalence of operators can be characterized by their behavior modulo compact operators. In simple terms, it says that if two operators are similar when ignoring small, compact differences, then they can be approximated by unitary transformations (think of "rotations" in a high-dimensional space). This helps mathematicians understand when operators are essentially the same in structure, even if they aren’t exactly identical, by focusing on their behavior outside of negligible, compact variations.