Analytic formulas for the hyperbolic distance between two contractions

• Autorzy: Ion Suciu
• Języki publikacji: EN

Abstrakty

EN

In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values strict contractions.

Słowa kluczowe

EN

Harnack parts; hyperbolic distance; operator Schwarz-Pick Lemma

Kategorie tematyczne

• 47A63: Operator inequalities
• 47A45: Canonical models for contractions and nonselfadjoint operators
• 30C80: Maximum principle; Schwarz's lemma, Lindel\"of principle, analogues and generalizations; subordination
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 239-252

Daty

wydano

1997

otrzymano

1995-07-12

Twórcy

autor

Ion Suciu

• Institute of Mathematics, Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania

Bibliografia

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• [12] I. Suciu, Analytic relations between functional models for contractions, Acta Sci. Math. (Szeged) 33 (1973), 359-365.
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• [14] I. Suciu, The Kobayashi distance between two contractions, in: Oper. Theory Adv. Appl. 61, Birkhäuser, Basel, 1993, 189-200.
• [15] I. Suciu and I. Valuşescu, On the hyperbolic metric on Harnack parts, Studia Math. 55 (1976), 97-109.
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