Central Morphisms and Envelopes of Holomorphy

Athanasios Kyriazis

Abstract: In this paper we study a particular class of continuous algebra morphisms the so-called $\bfc{C}$-central $\bfc{A}$-morphisms; i.e. continuous $\bfc{A}$-morphisms between topological $\bfc{A}$-algebras (viz. we take coefficients from a topological algebra $\bfc{A}$) such that their images have $\bfc{C}$-trivial center. In particular, we examine such morphisms for algebra-valued holomorphic functions on a complex manifold $X$, giving conditions that the set of the previous morphisms be the classical envelope of holomorphy of $X$.

Keywords: Central morphisms; envelopes of holomorphy; Runge pairs; inductive limits; tensor products; spectra.

Classification (MSC2000): 46M05, 32E15, 32E25; 46M40, 32E10

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