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Stein spaces characterized by their endomorphisms. (English) Zbl 1222.32023

In the frame of the questions concerning whether an analytic object is determined by the algebraic structures “naturally” arising from it such as algebras (or rings) of functions, the main result of the paper is the following: Let \(X\) and \(Y\) be complex spaces and \(\varphi: X \rightarrow Y\) an iso-conjugating map. Then \(\varphi\) is either holomorphic or antiholomorphic if the following criteria are fulfilled:
(1) \(X\) is a finite-dimensional Stein space;
(2) \(X\) admits a proper holomorphic embedding \( i: \mathbb C \hookrightarrow X\).
References to previous results and preliminaries necessary for the understanding of the question are presented. Several interesting examples and open questions are also discussed.

MSC:

32E10 Stein spaces
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References:

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