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19th International Conference on Operator Theory
June 27 - July 2, 2002
Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timisoara
Timisoara, Romania

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Hyperbolic structures on the Harnak parts of contractions
by
Ion Suciu
Institute of Mathematics of the Romanian Academy

Let H be a complex Hilbert space and A a contraction on H. As usual, DA is the defect operator of A and cal DA the defect space.

Consider the map
Psi A : cal B1(cal DA, cal DA*)rightarrow cal B(H)
defined by
Z rightarrow A+DAZ[I+A*Z]-1DA,     Zin cal B1(cal DA, cal DA*),
on the open unit ball of cal B(cal DA, cal DA*).

If H is finite dimensional, Im  PhiA is a ``simple" analytic manifold (open subset of an affine subspace of cal B(H) ) and ( Phi A)-1 is a global analytic cart.

We consider the attached hyperbolic metrics and compare them with the Harnack distance on the Harnack part generated by A.

Date received: June 10, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-53.