WHICH LINEAR TRANSFORMATIONS HAVE ISOMORPHIC HYPERINVARIANT SUBSPACE LATTICES

Abstract

Let A be a linear transformation on a finite-dimensional complex vector space with the associated algebra Alg A, commutant {A}', and hyperinvariant subspace lattice Hyperlat A. We determine Alg A, {A}' (up to algebra isomorphism), and Hyperlat A (up to lattice isomorphism) in terms of the parameters in the Jordan form of A.