Contractions with polynomial characteristic functions I. Geometric approach
Authors:
Ciprian Foias and Jaydeb Sarkar
Journal:
Trans. Amer. Math. Soc. 364 (2012), 41274153
MSC (2010):
Primary 47A45, 47A20, 47A48, 47A56
Published electronically:
March 13, 2012
Fulltext PDF
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Additional Information
Abstract: In this paper we study the completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions. These operators are precisely those which admit a matrix representation of the form where and are unilateral shifts of arbitrary multiplicities and is nilpotent. We prove that the dimension of ker and the dimension of are unitary invariants of and that , up to a quasisimilarity, is uniquely determined by . Also, we give a complete classification of the subclass of those contractions for which their characteristic functions are monomials.
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Additional Information
Ciprian Foias
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Jaydeb Sarkar
Affiliation:
Department of Mathematics, The University of Texas at San Antonio, San Antonio, Texas 78249
Address at time of publication:
Indian Statistical Institute, StatMath Unit, 8th Mile, Mysore Road, RVCE Post, Bangalore 560059, Karnataka, India
Email:
jay@isibang.ac.in, jaydeb@gmail.com
DOI:
http://dx.doi.org/10.1090/S00029947201205450X
PII:
S 00029947(2012)05450X
Keywords:
Characteristic function,
model,
weighted shifts,
nilpotent operators,
operatorvalued polynomials
Received by editor(s):
February 19, 2010
Received by editor(s) in revised form:
August 16, 2010
Published electronically:
March 13, 2012
Additional Notes:
This research was partially supported by a grant from the National Science Foundation. Part of this research was done while the second author was at Texas A&M University, College Station
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
