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, Volume 72, Issue 1, pp 257–274 | Cite as

A sufficient condition of type (Ω) for tame splitting of short exact sequences of Fréchet spaces

  • Markus Poppenberg


In a previous paper, the quotient spaces of (s) in the tame category of nuclear Fréchet spaces have been characterized by property (ΩDZ) corresponding to the topological condition (Ω) of D. Vogt and M. J. Wagner. In addition, a splitting theorem has been proved which provides the existence of a tame linear right inverse of a tame linear map on the assumption that the kernel of the given map has property (ΩDZ) and that certain tameness conditions hold. In this paper it is proved that property (Ω) in standard form (i.e., the dual norms ‖ ‖ n * are logarithmically convex) implies the tame splitting condition (ΩDZ) for any tamely nuclear Fréchet space equipped with a grading defined by sermiscalar products. As an application, property (ΩDZ) is verified for the kernels of any hypoelliptic system of linear partial differential operators with constant coefficients on ℝN or on a bounded convex region in ℝN.


Implicit Function Theorem Short Exact Sequence Quotient Space Linear Differential Operator Dual Norm 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Markus Poppenberg
    • 1
  1. 1.Fachbereich MathematikUniversität DortmundDortmundFederal Republic of Germany

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