Power Series Space Representations of Nuclear Frechet Spaces

DOI10.2307/2001342zbMath0724.46007OpenAlexW4243040475MaRDI QIDQ3211797

Dietmar Vogt

Publication date: 1990

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2001342

zbMATH Keywords

Fréchet space(\(\Omega \) )-spacecharacteristic of continuityfactors through a power series space of infinite typenuclear (DN)-spacenuclear spaces admitting a family of smoothing operatorsprojections in power series spacestame linear maptamely equivalent to power series spaces

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (13)

Tame spaces and power series spaces ⋮ A tame splitting theorem for exact sequences of Fréchet spaces ⋮ Negative results on the Nash-Moser theorem for Köthe sequence spaces and for spaces of ultradifferentiable functions ⋮ On the characterization of subspaces and quotient spaces of stable power series spaces of finite type ⋮ Characterization of the subspaces of (s) in the tame category ⋮ Tame sequence space representations of spaces of \(C^ \infty\)-functions ⋮ On operators and complemented subspaces in the Köthe spaces determined by sparse matrices ⋮ A sufficient condition of type \((\Omega{})\) for tame splitting of short exact sequences of Fréchet spaces ⋮ Simultaneous smoothing and interpolation with respect to E. Borel's theorem ⋮ An Inverse Function Theorem for Fréchet Spaces Satisfying a Smoothing Property and (DN) ⋮ On complemented subspaces of non-Archimedean Köthe spaces ⋮ Tameness in Fréchet spaces of analytic functions ⋮ Complemented subspaces of sums and products of Banach spaces

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