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The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of C * -algebras

Kazimierz Włodarczyk (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 J * -algebras. Since J * -algebras are natural generalizations of C * -algebras, B * -algebras, J ⁢ C * -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ℂ n 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.

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