An inverse function theorem for Fréchet spaces admitting generalized smoothing operators

DOI10.1307/mmj/1029005469zbMath0883.46026OpenAlexW2010119830MaRDI QIDQ1923904

Markus Poppenberg

Publication date: 23 February 1998

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1029005469

zbMATH Keywords

Newton's methodFréchet spaceKöthe sequence spacesproperty \((\Omega)\)existence of smoothing operatorsgeneralized smoothing operatorsinverse function theorem of the Nash-Moser typetopological conditions \((DN)\)

Mathematics Subject Classification ID

Locally convex Fréchet spaces and (DF)-spaces (46A04) Derivatives of functions in infinite-dimensional spaces (46G05)

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Negative results on the Nash-Moser theorem for Köthe sequence spaces and for spaces of ultradifferentiable functions, An Inverse Function Theorem for Fréchet Spaces Satisfying a Smoothing Property and (DN)