Contractions with Polynomial characteristic functions I. Geometric approach

Details Contractions with Polynomial characteristic functions I. Geometric approach Contractions with Polynomial characteristic functions I. Geometric approach

2010-02-19

arxiv.org/abs/1002.3679v2

Mathematics

Functional Analysis

29 pages. Typos corrected. Proposition 3.8 is new. To appear in Transactions of the American Mathematical Society

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Contractions with Polynomial characteristic functions I. Geometric approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Contractions with Polynomial characteristic functions I. Geometric approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Contractions with Polynomial characteristic functions I. Geometric approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-363379