Inductive limits and ...-tensor products.
Isomorphic classification of the tensor products
It is proved, using so-called multirectangular invariants, that the condition αβ = α̃β̃ is sufficient for the isomorphism of the spaces and . This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].
Isomorphism of the co-universal F-spaces of Kalton and Terry
Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces
Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory...
Köthe coechelon spaces as locally convex algebras
We study those Köthe coechelon sequence spaces , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals...
Köthe spaces modeled on spaces of functions
The isomorphic classification problem for the Köthe models of some function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant and other invariants related to the “quantity” characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property are not isomorphic.
L’équation dans les ouverts pseudo-convexes des espaces DFN
Lifting uniformly continuous maps with values in nuclear Fréchet spaces
Lifting-Sätze für Vektorfunktionen und (EL)-Räume.
Linear topological invariants of spaces of holomorphic functions in infinite dimension.
It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...
Local convexity is a three-space property for non-archimedean Fréchet spaces
Local convexity of twisted sums
Localization of bounded sets in tensor products.
The problem of topologies of Grothendieck is considered for complete tensor products of Fréchet spaces endowed with the topology defined by an arbitrary tensor norm. Some consequences on the stability of certain locally convex properties in spaces of operators are also given.
Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces
Mittag-Leffler methods in analysis.
In this survey we present two Mittag-Leffler lemmas and several applications to topics as varied as the delta-equation, Fréchet algebras, inductive limits of Banach spaces and quasi-normable Fréchet spaces.
Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces
For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the and topologies on ℋ (U).
Non-natural topologies on spaces of holomorphic functions
It is shown that every proper Fréchet space with weak*-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.
Non-Schwartzian Power Series Spaces.
Nuclear Fréchet Spaces with Locally Round Finite Dimensional Decompositions.
Nuclear Fréchet spaces without the bounded approximation property