1. CJM Online first
|Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$|
We obtain results on the unitary equivalence of weak contractions of class $C_0$ to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool is the theory of boundary representations due to Arveson. We also generalize and improve previously known results concerning unitary equivalence and similarity to Jordan models when the minimal function is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence
2. CJM 2006 (vol 58 pp. 1291)
|The General Structure of $G$-Graded Contractions of Lie Algebras I. The Classification |
We give the general structure of complex (resp., real) $G$-graded contractions of Lie algebras where $G$ is an arbitrary finite Abelian group. For this purpose, we introduce a number of concepts, such as pseudobasis, higher-order identities, and sign invariants. We characterize the equivalence classes of $G$-graded contractions by showing that our set of invariants (support, higher-order identities, and sign invariants) is complete, which yields a classification.
Keywords:Lie algebras, graded contractions