Projective limits of perfect measure spaces
Quasi-incomplete regular LB-space.
Regular Fréchet-Lie groups of invertible elements in some inverse limits of unital involutive Banach algebras.
Regularity of general weighted inductive limits.
Sequential retractivities and regularity on inductive limits
In this paper we prove the following result: an inductive limit is regular if and only if for each Mackey null sequence in there exists such that is contained and bounded in . From this we obtain a number of equivalent descriptions of regularity.
Sobre espacios (LF) metrizables.
Solution of a problem of Grothendieck.
Spaces C(X) and L(μ) as direct or inverse limits in the category of Banach spaces
Stable elements of Banach and Fréchet algebras
We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.
Stable inverse-limit sequences and automatic continuity
The elementary theory of stable inverse-limit sequences, introduced in stable inverse-limit sequences, is used to extend the 'stability lemma' of automatic continuity theory.
Stable inverse-limit sequences, with application to Predict algebras
The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.
Strict inductive and projective limits, twisted spaces and quojections
Tensor Sequences and Inductive Limits with Local Partition of Unity.
Teoria directa das distribuições sobre uma variedade
The dual of the space of holomorphic functions on locally closed convex sets.
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
The exactness of the projective limit functor on the category of quotients of Frechet spaces
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
The Poulsen simplex is not a tensor product.
The projective limit functor for spectra of webbed spaces
We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
The universal Banach space with a -suppression unconditional basis
Using the technique of Fraïssé theory, for every constant , we construct a universal object in the class of Banach spaces possessing a normalized -suppression unconditional Schauder basis.
Topologies et compactologies