Abstract
The Kobayashi pseudodistance can be defined on each complex Banach manifold. Using contractive analytic functions from the unit disk into B(H) we can define the Kobayashi pseudodistance on the closed unit ball B 1 of B(H), where B(H) is the algebra of all bounded linear operators on the Hubert space H. The main result of the paper asserts the fact the Kobayashi pseudodistance is a true distance on the Shmuiyan parts of B 1. Some connections between Pick condition for the two-nodes Nevanlinna-Pick interpolation problem and the Kobayashi distance are established.
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© 1993 Springer Basel AG
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Suciu, I. (1993). The Kobayashi Distance between two Contractions. In: Gheondea, A., Timotin, D., Vasilescu, FH. (eds) Operator Extensions, Interpolation of Functions and Related Topics. Operator Theory: Advances and Applications, vol 61. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8575-1_11
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DOI: https://doi.org/10.1007/978-3-0348-8575-1_11
Publisher Name: Birkhäuser, Basel
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