0608087v2.pdf (372.73 kB)
Download fileClosed graph and open mapping theorems for topological ℂ̃-modules and applications
journal contribution
posted on 2015-04-20, 11:29 authored by Claudia GarettoWe present closed graph and open mapping theorems for ℂ̃-linear maps acting between suitable classes of topological and locally convex topological ℂ̃-modules. This is done by adaptation of De Wilde's theory of webbed spaces and Adasch-Ernst-Keim's theory of barrelled spaces to the context of locally convex and topological ℂ̃-modules, respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach ℂ̃-modules. In particular we obtain a necessary condition for G{script}ς-hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Funding
This work was supported by FWF (Austria), Grants T305-N13 and Y237-N13, and TWF (Tyrol), Grant UNI-0404/305.
History
School
- Science
Department
- Mathematical Sciences
Published in
Mathematische NachrichtenVolume
282Issue
8Pages
1159 - 1188Citation
GARETTO, C., 2009. Closed graph and open mapping theorems for topological ℂ̃-modules and applications. Mathematische Nachrichten, 282 (8), pp. 1159 - 1188.Publisher
© WILEY-VCH Verlag GmbH & Co.Version
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2009Notes
This is the accepted version of the following article: GARETTO, C., 2009. Closed graph and open mapping theorems for topological ℂ̃-modules and applications. Mathematische Nachrichten, 282 (8), pp. 1159 - 1188, which has been published in final form at: http://dx.doi.org/10.1002/mana.200610793ISSN
0025-584XeISSN
1522-2616Publisher version
Language
- en