Domains of Analytic Existence in Real Frechet Spaces

摘要

If E is a real separable Frechet space, we prove that every non void domain #OMEGA# of E which is open for a continuous semi-norm is a domain of analytic existence. In particular, every non void, open and convex subset #OMEGA# of E is a domain of analytic existence. Moreover, this result cannot be improved in the case of an arbitrary real separable Frechet space. In fact, in the space #omega# of real sequences, a non void domain #OMEGA# is a domain of analytic existence if and only if #OMEGA# is open for a continuous semi-norm.