A sufficient condition for vanishing of the derived projective limit functor

DOI10.1007/BF01197593zbMath0859.46046OpenAlexW2063080683MaRDI QIDQ1924981

Jochen Wengenroth, Leonhard Frerick

Publication date: 7 April 1997

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01197593

zbMATH Keywords

Fréchet spacesprojective limit functorprojective spectrumsurjectivity of convolution operatorscategory of locally convex spacessplitting theory for Fréchet spaces

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Categories, functors in functional analysis (46M15)

Related Items (18)

Spaces of \(N\)-homogeneous polynomials between Fréchet spaces ⋮ Splitting of exact sequences of Fréchet spaces in the absence of continuous norms ⋮ Strong duals of projective limits of (LB)-spaces ⋮ A conjecture of Palamodov about the functors \(\text{Ext}^{k}\) in the category of locally convex spaces. ⋮ Real analytic parameter dependence of solutions of differential equations over Roumieu classes ⋮ Topological properties of kernels of partial differential operators ⋮ Characterization of splitting for Fréchet--Hilbert spaces via interpolation ⋮ Splitting and parameter dependence in the category of \(\mathrm{PLH}\) spaces ⋮ The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations ⋮ A homological approach to the splitting theory of \(\mathrm{PLS}_{\mathrm{w}}\) spaces ⋮ Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space ⋮ Real analytic parameter dependence of solutions of differential equations ⋮ On the splitting relation for Fréchet-Hilbert spaces ⋮ Projective limits of weighted LB-spaces of holomorphic functions ⋮ Real analytic curves in Fréchet spaces and their duals ⋮ PLB-spaces of holomorphic functions with logarithmic growth conditions ⋮ A generalization of a theorem of A. Grothendieck ⋮ Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences

Cites Work

• The splitting relation for Köthe spaces
• Existence of Fundamental Solutions and Surjectivity of Convolution Operators on Classes of Ultra-Differentiable Functions
• Acyclic inductive spectra of Fréchet spaces
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