A remark on projective limits of function spaces
Abstract
Let Omega subset of Cd be an open set and Km, m = 1, 2, . . . an exhaustion of Omega by compact subsets of Omega. We set Omegam = int(Km) and let Xm(Omegam) be a topological space of holomorphic functions on Omegam between A infinity (Omegam) and H(Omegam). Then we show that the projective limit of the family Xm(Omegam), m = 1, 2, . . . , under the restriction maps is homeomorphic and linearly isomorphic to the Frechet space H(Omega), idependently of the choice of the spaces Xm(Omegam).
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