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Classification of Cyclic Invariant Subspaces of Jordan Operators

Hari Bercovici, Thomas Smotzer

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Abstract

Let T be an operator of class C 0 and M a cyclic invariant subspace for T . We show that the weakly quasiaffine orbit of M is determined by the quasisimilarity classes of the restriction T ∣ M and of the compression T M ⊥ = (T* ❘ M ∣ )* . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Let T be an operator of class C 0 and M a cyclic invariant subspace for T . We show that the weakly quasiaffine orbit of M is determined by the quasisimilarity classes of the restriction T ∣ M and of the compression T M ⊥ = (T* ❘ M ∣ )* . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Available abstract

Let T be an operator of class C 0 and M a cyclic invariant subspace for T . We show that the weakly quasiaffine orbit of M is determined by the quasisimilarity classes of the restriction T ∣ M and of the compression T M ⊥ = (T* ❘ M ∣ )* . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Key concepts: Linear subspace, Invariant (physics), Reflexive operator algebra, Invariant subspace, Mathematics, Subspace topology, Pure mathematics, Combinatorics

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