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On the CR-structure of certain linear group orbits in infinite dimensions. (English) Zbl 1170.32314
Summary: 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 of the author and D. Zaitsev [Invent. Math. 153, No. 1, 45–104 (2003; Zbl 1027.32032)].
##### MSC:
 32V25 Extension of functions and other analytic objects from CR manifolds 17C50 Jordan structures associated with other structures 32H02 Holomorphic mappings on analytic spaces; holomorphic embeddings; related questions 32E20 Polynomial convexity 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces) 46G20 Infinite dimensional holomorphy