On the functors Ext¹(E,F) for Fréchet spaces

DOI10.4064/sm-85-2-163-197zbMath0651.46001OpenAlexW339862298MaRDI QIDQ3796180

Publication date: 1987

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/218745

zbMATH Keywords

Köthe space nuclear Fréchet spaces derived functors quasinormable spaces acyclicity classes category of Fréchet spaces extension and lifting of linear operators invariants (DN) and (\(\Omega\))short exact sequences of nuclear Fréchet spaces spaces of holomorphic functions on a connected N-dimensional Stein manifold spaces of solutions of elliptic linear partial differential operators Splitting theorems stable power series spaces zero solutions of elliptic linear partial differential operators with constant coefficients

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Projective and injective objects in functional analysis (46M10) General theory of PDEs and systems of PDEs with constant coefficients (35E20) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Duality theory for topological vector spaces (46A20) Spaces of linear operators; topological tensor products; approximation properties (46A32) Inductive and projective limits in functional analysis (46M40) Categories, functors in functional analysis (46M15) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (23)

Spaces of \(N\)-homogeneous polynomials between Fréchet spaces ⋮ Splitting of exact sequences of Fréchet spaces in the absence of continuous norms ⋮ Surjectivity of the ̄∂-operator between weighted spaces of smooth vector-valued functions ⋮ Extensions of tempered representations ⋮ Weighted (\textit{PLB})-spaces of ultradifferentiable functions and multiplier spaces ⋮ Commutative subalgebras of the algebra of smooth operators ⋮ Parameter dependence of solutions of the Cauchy-Riemann equation on weighted spaces of smooth functions ⋮ Extension operators for analytic functions defined on certain closed subvarieties of a Stein space ⋮ One-sided ideals of the non-commutative Schwartz space ⋮ A conjecture of Palamodov about the functors \(\text{Ext}^{k}\) in the category of locally convex spaces. ⋮ Linear topological invariants for kernels of convolution and differential operators ⋮ Topological properties of convolutor spaces via the short-time Fourier transform ⋮ Splitting and parameter dependence in the category of \(\mathrm{PLH}\) spaces ⋮ Automatic continuity and amenability in the non-commutative Schwartz space ⋮ 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 ⋮ The Borel-Ritt problem in Beurling ultraholomorphic classes ⋮ Note on the reproducing property of the Bergman kernel ⋮ A splitting theorem for the space of smooth functions ⋮ Quasinormable \(C_0\)-groups and translation-invariant Fréchet spaces of type \(\mathcal{D}_E\) ⋮ The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes ⋮ Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences ⋮ Parameter dependence of solutions of partial differential equations in spaces of real analytic functions

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