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 explicitly and show as main result that every continuous CR-function on 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.
Kaup, Wilhelm 1
@article{ASNSP_2004_5_3_3_535_0,
author = {Kaup, Wilhelm},
title = {On the {CR-structure} of certain linear group orbits in infinite dimensions},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {535--554},
year = {2004},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {3},
mrnumber = {2099248},
zbl = {1170.32314},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2004_5_3_3_535_0/}
}
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 SP - 535 EP - 554 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2004_5_3_3_535_0/ LA - en ID - ASNSP_2004_5_3_3_535_0 ER -
%0 Journal Article %A Kaup, Wilhelm %T On the CR-structure of certain linear group orbits in infinite dimensions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 535-554 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2004_5_3_3_535_0/ %G en %F ASNSP_2004_5_3_3_535_0
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. https://www.numdam.org/item/ASNSP_2004_5_3_3_535_0/
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