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I am looking for a detailed account, in English or French, of the main result and its proof from this paper by O. Forster

Zur Theorie der Steinschen Algebren und Moduln, Mathematische Zeitschrift 97, 376-405, 1967.

The main result of this article is an equivalence of categories between certain Stein spaces and their Frechet algebras of global functions. Does anyone know where I can find this result (or a generalization of it) proven in English or French?

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Look at Grauert Remmert Theory of Stein spaces . – Mohan Ramachandran Aug 2 '13 at 17:18

Forster's result can be seen as the Serre-Swan theorem for Stein manifolds. A proof and many details can be found, among other references, in the thesis of A. S. Morye "On the Serre-Swan Theorem and on Vector Bundles over Real Abelian Varieties". Section $2.3.5$ reviews Forster's result on a few pages. It is more or less deduced from the other results. However, I am not sure, if you find this satisfying. Another discussion in this direction can be found here: Holomorphic vector bundles and Swan's theorem.

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