Lifting uniformly continuous maps with values in nuclear Fréchet spaces
Lifting-Sätze für Vektorfunktionen und (EL)-Räume.
Limited spaces
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...
Lokalkonvexe Sequenzen mit kompakten Abbildungen.
l(Φ,φ) operators and (Φ,φ)-spaces.
A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...