Parametrization of invariant subspaces of unitary operators
by
Laszlo Kerchy
Bolyai Institute, University of Szeged, Hungary

Classical theorems, due to Wiener and Helson in the case of reducing subspaces and to Beurling, Lax, Halmos in the case of nonreducing subspaces, describe the invariant subspaces of a general unitary operator U. However, this description is of limited value when we want to study the lattice theoretic structure of the invariant subspace lattice LatU. We propose a parametrization of LatU which makes the inclusion relation more transparent. This parametrization is applied to answer questions, posed by J. B. Conway and T. A. Gillespie on the characterization of isometries having isomorphic invariant subspace lattices.

Date received: May 31, 2000