Quasisimilarity of Invariant Subspaces for Uniform Jordan Operators of Infinite Multiplicity

Abstract

Let T be a bounded linear operator on a separable Hilbert space H, and let M and N be two invariant subspaces for T. We will say that M and N are quasisimilar if there exist quasiaffinities (i.e. bounded one-to-one operators with dense ranges) X and Y, commuting with T, such that (

Cyclic row contractions and rigidity of invariant subspaces

“…Such inquiries generate significant interest in the setting of Hilbert modules on reproducing kernel Hilbert spaces; see [14] and the references therein. Our work on this topic initiates a multivariate exploration of equivalence classes of invariant subspaces for constrained contractions, as studied in [11], [9], [10], [28], [15], [16].…”

Quasisimilarity of invariant subspaces for $C_0$ operators with multiplicity two

“…Later on, it was proved in [2] that this classification of invariant subspaces of a uniform Jordan operator holds if and only if T |M has property (P). In general, the quasisimilarity class of an invariant subspace for a uniform Jordan operator is determined by the quasisimilarity classes of the restriction T |M and of the compression T M ⊥ (see [3]).…”