Extreme fixed points of operator LFT, applications to the Königs problem

We proceed with our study of the Königs problem (KE-problem), which was initiated and developed by several authors. We show that a wide class of fractional-linear mappings with a fixed point on the boundary of the unit operator ball D have the KE-property. This means that each mapping from this clas...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 71; no. 12; pp. e2517 - e2520
Main Authors: Khatskevich, V.A., Senderov, V.A.
Format: Journal Article
Language:English
Published: Elsevier Ltd 15.12.2009
Subjects:
Continuous one-parameter semigroup
Indefinite metric
Krein space
Linear operator
Krein space
Indefinite metric
Linear operator
primary
Continuous one-parameter semigroup
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary:We proceed with our study of the Königs problem (KE-problem), which was initiated and developed by several authors. We show that a wide class of fractional-linear mappings with a fixed point on the boundary of the unit operator ball D have the KE-property. This means that each mapping from this class can be included in some semigroup of holomorphisms of D which is continuous in the topology of locally uniform (over D ) convergence.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.05.049