$C\_\{\textperiodcentered 0\}$-contractions: a Jordan model and lattices of invariant subspaces

Abstract

Abstract. A subclass C ·0 (C 0 (P ), fin) of the class of C ·0 -contractions is introduced and studied. This subclass is a generalization of the subclass of C ·0 -contractions with finite defect indices, and it includes the C ·0 -contractions T for which dim Ker T * < ∞ and the defect operator (I − T * T ) 1/2 belongs to the Hilbert-Schmidt class. For an operator of class C ·0 (C 0 (P ), fin), a Jordan model is constructed, and it is proved that the lattices of invariant subspaces remain isomorphic under the quasiaffine transformations.