Geodesic
On the CR-structure of certain linear group orbits in infinite dimensions
Kaup, Wilhelm1
1 Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 535-554

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For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits M explicitly and show as main result that every continuous CR-function on M has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite dimensions results from a recent joint paper with D. Zaitsev in Inventiones math. 153, 45-104.

Classification : 32V25, 17C50, 32H02, 32E20, 32M15, 46G20

Kaup, Wilhelm 1

1 Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany 
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     title = {On the {CR-structure} of certain linear group orbits in infinite dimensions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Kaup, Wilhelm. On the CR-structure of certain linear group orbits in infinite dimensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 535-554. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_535_0/