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, p. 535-554
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
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {3},
     year = {2004},
     pages = {535-554},
     zbl = {1170.32314},
     mrnumber = {2099248},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/ASNSP_2004_5_3_3_535_0/

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