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The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in -algebras. Since -algebras are natural generalizations of -algebras, -algebras, -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.
We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.
The paper contains the formulation of the problem and an almost up-to-date survey of some results in the area.
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
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