2010/02/19 by Ciprian Foiaş, Ciprian Foias, Jaydeb Sarkar +2
Mathematics · #47A20 #47A45 #47A48 #47A56 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:47A20 #msc:47A45 #msc:47A48 #msc:47A56
paper · pdf · doi:10.48550/arxiv.1002.3679
29 pages. Typos corrected. Proposition 3.8 is new. To appear in Transactions of the American Mathematical Society
openalex publication_date 2010/02/19 · arxiv created 2010/08/26 · arxiv updated 2010/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we study the completely non unitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions. These operators are precisely those which admit a matrix representation of the form T = S & * & * 0 & N & * 0& 0& C, where S and C^* are unilateral shifts of arbitrary multiplicities and N is nilpotent. We prove that dimension of ker S^* and dimension of ker C are unitary invariants of T and that N, up to a quasi-similarity is uniquely determined by T. Also, we give a complete classification of the subclass of those contractions for which their characteristic functions are monomials.