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This paper establishes the Gleason result for finitely generated ideals inthe context of Frechet algebras, and, in particular, provides an affirmativeanswer to a question about the Gleason result in commutative Frechet algebras(Carpenter posed this question for uniform Frechet algebras in 1970). As awelcome bonus of our method, locally Stein algebras are completelycharacterized, and, as an application of this characterization, an affirmativeanswer to the Gleason problem (1964) for such algebras is provided recapturingall the classical results on the Gleason problem in the theory of severalcomplex variables.

On functional analytic approach for Gleason problem in the theory of SCV