Journal of Mathematical Sciences

, Volume 192, Issue 4, pp 426–440 | Cite as

Operator linear-fractional relations: main properties, some applications

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Abstract

We consider operator linear-fractional relations of the form
$$ F(K)=\left\{ {Q:A+BK=Q\left( {C+DK} \right)} \right\}, $$
where A, B, C, D, K, and Q are operators between Hilbert spaces. If C + DK is invertible, the relation F becomes a linear-fractional transformation. In the case where F is the automorphism of a unit operator ball, we study the conditions for F to be represented in the form of a composition of an automorphism and an affine relation. The results obtained are applied to the Abel–Schröder equations, Königs embedding problem, and some other questions.

Keywords

Operator linear-fractional relation factorization Königs problem Abel–Schröder equation 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics ORT Braude Academic CollegeKarmielIsrael

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