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Title: Closed graph and open mapping theorems for topological ℂ̃-modules and applications
Authors: Garetto, Claudia
Keywords: Closed graph theorem
Colombeau algebras
Topological modules
Issue Date: 2009
Publisher: © WILEY-VCH Verlag GmbH & Co.
Citation: GARETTO, C., 2009. Closed graph and open mapping theorems for topological ℂ̃-modules and applications. Mathematische Nachrichten, 282 (8), pp. 1159 - 1188.
Abstract: 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.
Description: 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
Sponsor: This work was supported by FWF (Austria), Grants T305-N13 and Y237-N13, and TWF (Tyrol), Grant UNI-0404/305.
Version: Accepted for publication
DOI: 10.1002/mana.200610793
URI: https://dspace.lboro.ac.uk/2134/17312
Publisher Link: http://dx.doi.org/10.1002/mana.200610793
ISSN: 0025-584X
Appears in Collections:Published Articles (Maths)

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