Quasi-similarity of contractions having a 2 × 1 characteristic function
Sergio Bermudo
Universidad Pablo de Olavide, Sevilla, SpainCarmen H. Mancera
Universidad de Sevilla, SpainPedro J. Paúl
Universidad de Sevilla, SpainVasily Vasyunin
Steklov Mathematical Institute, St. Petersburg, Russian Federation
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Abstract
Let be a completely non-unitary contraction having a non-zero characteristic function which is a column vector of functions in . As it is well-known, such a function can be written as where are such that is an outer function with , is an inner function, , and (here stands for the greatest common inner divisor). Now consider a second completely non-unitary contraction having also a characteristic function . We prove that is quasi-similar to if, and only if, the following conditions hold:
- ,
- a.e., and
- the ideal generated by and in the Smirnov class equals the corresponding ideal generated by and .
Cite this article
Sergio Bermudo, Carmen H. Mancera, Pedro J. Paúl, Vasily Vasyunin, Quasi-similarity of contractions having a 2 × 1 characteristic function. Rev. Mat. Iberoam. 23 (2007), no. 2, pp. 677–704
DOI 10.4171/RMI/509