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Décompositions dans certaines algèbres de Fréchet de fonctions holomorphes.

Ahmed Sebbar (1994)

Revista Matemática Iberoamericana

Dans ce travail, nous étudions le problème de décomposicion suivant: Étant donnés deux ouverts bornés de Cp, Ω1 et Ω2 (vérifiant certaines conditions) et étant donnée une matrice A(z), carrée d'ordre n, dont les coefficients sont des fonctions holomorphes dans Ω1 ∩ Ω2, ayant une prolongement C∞ à l'adhérence (Ω1 ∩ Ω2), peut-on trouver deux matrices A1(z), A2(z) holomorphes dans Ω1 et Ω2 respectivement et se prolongeant de manière C∞ à (Ω1) et (Ω2) telles que sur Ω1 ∩ Ω2 on aitA = A1A2.

Diameter-preserving maps on various classes of function spaces

Bruce A. Barnes, Ashoke K. Roy (2002)

Studia Mathematica

Under some mild assumptions, non-linear diameter-preserving bijections between (vector-valued) function spaces are characterized with the help of a well-known theorem of Ulam and Mazur. A necessary and sufficient condition for the existence of a diameter-preserving bijection between function spaces in the complex scalar case is derived, and a complete description of such maps is given in several important cases.

Dimensional compactness in biequivalence vector spaces

J. Náter, P. Pulmann, Pavol Zlatoš (1992)

Commentationes Mathematicae Universitatis Carolinae

The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a π -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set s and classes of set functions s → Q ...

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