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Closed graph and open mapping theorems for topological ℂ̃-modules and applications

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journal contribution
posted on 20.04.2015, 11:29 by Claudia Garetto
We 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 Nachrichten

Volume

282

Issue

8

Pages

1159 - 1188

Citation

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

2009

Notes

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.200610793

ISSN

0025-584X

eISSN

1522-2616

Language

en