Don Hadwin - Finitely strongly reductive operators

Abstract: A Hilbert space operator is finitely strongly reductive () if every sequence of approximately invariant finite-dimensional subspaces is approximately reducing. Not every normal operator is (e.g., the approximate point spectrum must have empty interior), not every operator is normal ( e.g., isometries are ). We obtain some results (e.g., every essentially normal quasitriangular fsr operator is normal), and pose some interesting open problems.