Real closed rings, I. Residue rings of rings of continuous functions
Remarks on -subalgebras of
Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of containing...
Representation of locally convex algebras.
We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.
Ring homomorphisms on H(G).
Rings of continuous functions with values in a non-archimedean ordered field
Rings of continuous functions with values in an archimedean ordered field
Schauder Type Theorems for Differentiable and Holomorphic Mappings.
Separating maps and the nonarchimedean Hewitt theorem
Sequence space representations for (FN)-algebras of entire functions modulo closed ideals
Simultaneous stabilization in
We study the problem of simultaneous stabilization for the algebra . Invertible pairs , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since has stable rank two, we are faced here with a different situation....
Solution d'un problème d'Erdös, Gillman et Henriksen et application à l'étude des homomorphismes de C-(K).
Sous-espaces privilégiés d'un polycylindre
Cet article précise la notion de privilège introduite par A. Douady. Un sous-espace privilégié d’un polycylindre est défini par un idéal fermé de l’algèbre des fonctions continues sur et holomorphes sur , cet idéal étant supposé de résolution finie.Les sous-espaces privilégiés d’un polycylindre fixé sont classés par un espace analytique banachique, “une grassmannienne”, introduit par A. Douady et dont on donne ici la propriété universelle.Pour cela on montre que la notion de privilège est locale...
Spectral study of holomorphic functions with bounded growth
This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.
Spectral Theory for A (X).
Strict continuous homomorphisms on spaces of bounded holomorphic functions.
Let HE∞ be the space of all bounded holomorphic functions on the unit ball of the Banach space E. In this note we study the algebra homomorphisms on HE∞ which are strict continuous.
Strict topologies as topological algebras
Let be a completely regular Hausdorff space, the space of all scalar-valued bounded continuous functions on with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally -convex.
Structure de Frobenius faible pour les équations différentielles du premier ordre
Structure spaces for rings of continuous functions with applications to realcompactifications
Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Super real closed rings
A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by...
Sur la division et la composition dans des classes ultradifférentiables
We generalize to some classes of ultradifferentiable jets or functions the classical Łojasiewicz Division Theorem and Glaeser Composition Theorem. The proof uses the desingularization results by Hironaka, Bierstone and Milman.