Continuity properties of Hyperlat and reducing subspaces
Let V be a finite dimensional complex vector space of dimension \(n\geq 2\), and let A be a linear operator on V. A subspace M is hyperinvariant if it is invariant under every linear operator which commutes with A. Further M is reducing if it is invariant and has an invariant complement. Let RED be the set valued map which associates with each linear transformation A the set of all reducing subspaces. Define HYPERLAT similarly. The author determines the points of continuity, upper semicontinuity, and lower semicontinuity of these two set valued maps.
scientific article; zbMATH DE number 4165067
scientific article