Geometry of nuclear spaces. II - Linear topological invariants
Geometry of nuclear spaces. III - Spaces of holomorphic functions
Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Holomorphic functions on fully nuclear spaces
Holomorphic functions on strict inductive limits of Banach spaces.
In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Ideals in a C*-Algebra.
Inductive limit topologies on Orlicz spaces
Let be an Orlicz space defined by a convex Orlicz function and let be the space of finite elements in (= the ideal of all elements of order continuous norm). We show that the usual norm topology on restricted to can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on .
*-inductive limits and partition of unity.
Inductive Limits and Partitions of Unity.
Infinite-factorable holomorphic mappings on locally convex spaces.
Interpolation d'opérateurs entre espaces de fonctions holomorphes
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...
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...
La categorie Abelienne des quotients de type
We construct the category of quotients of -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.
(LF)-Spaces, Quasi-Baire Spaces and the Strongest Locally Convex Topology.
Lifting-Sätze für Vektorfunktionen und (EL)-Räume.
Limits and the Ext functor.
L'induction topologique
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...
Manifolds of smooth maps