A remark on projective limits of function spaces
Complex Variables
2017-04-20 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
Let Omega subset of C^d be an open set and Km, m = 1, 2, . . . an exhaustion of Omega by compact subsets of Omega. We set Omega_m = int(Km) and let Xm(Omega_m) be a topological space of holomorphic functions on Omega_m between A^ infinity (Omega_m) and H(Omega_m). Then we show that the projective limit of the family Xm(Omega_m), 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(Omega_m).
Keywords
Cite
@article{arxiv.1704.05780,
title = {A remark on projective limits of function spaces},
author = {Aggeliki Kampoukou and Vassili Nestoridis},
journal= {arXiv preprint arXiv:1704.05780},
year = {2017}
}