Abstract
For an operator T on a Hilbert space let Hyperlat T denote its hyperinvariant subspace lattice. Assume that T is a completely nonunitary C1l contraction with finite defect indices. In this note we characterize the elements of Hyperlat T among invariant subspaces for T in terms of their corresponding regular factorizations and show that elements in Hyperlat T are exactly the spectral subspaces of T defined by Sz.-Nagy and Foias. As a corollary, if T7, T2 are two such operators which are quasi-similar to each other, then Hyperlat T, is Qattice) isomorphic to Hyperlat T2.
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