On the CR-structure of certain linear group orbits in infinite dimensions

Wilhelm Kaup[1]

  • [1] Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 3, page 535-554
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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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 3.3 (2004): 535-554. <http://eudml.org/doc/84539>.

@article{Kaup2004,
abstract = {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.},
affiliation = {Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany},
author = {Kaup, Wilhelm},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {535-554},
publisher = {Scuola Normale Superiore, Pisa},
title = {On the CR-structure of certain linear group orbits in infinite dimensions},
url = {http://eudml.org/doc/84539},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Kaup, Wilhelm
TI - On the CR-structure of certain linear group orbits in infinite dimensions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 3
SP - 535
EP - 554
AB - 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.
LA - eng
UR - http://eudml.org/doc/84539
ER -

References

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  12. [12] W. Kaup, Bounded symmetric domains and polynomial convexity, Manuscripta Math. 114 (2004), 391-398. Zbl1056.32011MR2076455
  13. [13] W. Kaup – D. Zaitsev, On the CR-structure of compact group orbits associated with bounded symmetric domains, Invent. Math. 153 (2003), 45-104. Zbl1027.32032MR1990667
  14. [14] O. Loos, “Jordan pairs”, Springer Lecture Notes 460, 1975. Zbl0301.17003MR444721
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  16. [16] J. Sauter, “Randstrukturen beschränkter symmetrischer Gebiete”, Dissertation, Tübingen, 1995. 

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