On two classes of LF-spaces
On weighted inductive limits of non-Archimedean spaces of continuous functions
Si studiano alcune proprietà di un certo limite induttivo di spazi non-archimedei di funzioni continue. In particolare, si esamina la completezza di questo limite induttivo e si indaga il problema di quando lo spazio coincide con il proprio inviluppo proiettivo.
On Weighted Inductive Limits of Spaces of Continuous Function.
Open Subsets of LF-spaces
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
Polynomials and multilinear forms on fully nuclear spaces
Pontryagin Duality for Subgroups and Quotients of Nuclear Spaces.
Preduals of Sobolev-Campanato spaces
We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.
Preservation of fast completeness under inductive limits
Projective representations of spaces of quasianalytic functionals
The weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier-Laplace transform of the space of analytic functionals on an open convex subset of can be described algebraically as the intersection of a family of weighted Banach spaces of entire functions. The corresponding result for the spaces of quasianalytic functionals is also derived.
Quasi-bounded sets.
Quasi-distinguished and boundedly completed locally convex spaces.
Quasi-incomplete regular LB-space.
Quelques applications des éspaces de Silva et de leurs duals
Quotient spaces defined by linear relations
Quotient spaces of (s) with basis
Quotientenräume von stabilen Potenzreihenräumen endlichen Typs.
Real Analytic Curves in Fréchet Spaces and Their Duals.
Reflexivity of inductive limits
An inductive locally convex limit of reflexive topological spaces is reflexive iff it is almost regular.
Regular inductive limits of K-spaces.
A well-known result for bounded sets in inductive limits of locally convex spaces is the following: If each of the constituent spaces En are Fréchet spaces and E is the inductive limit of the spaces En, then each bounded subset of E is bounded in some En iff E is locally complete. Using DeWilde's localization theorem, we show here that the completeness of each En and the local completeness of E may be replaced with the conditions that the spaces En are all webbed K-spaces and E is locally Baire,...
Regularity, barrelledness and dual strong unions in locally convex spaces.