𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Intermediate algebras between C∗(X) and C(X) as rings of fractions of C∗(X)

✍ Scribed by J.M. Domínguez; J. Gómez; M.A. Mulero

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
544 KB
Volume
77
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

Let C(X) be the algebra of all K-valued continuous functions on a topological space X (with = ~. or K = C) and C*(X) the subalgebra of bounded functions. This paper deals with subalgebras of C(X) containing C'(X). We prove that these subalgebras are exactly the rings of fractions of C'(X) with respect to muhiplicatively closed subsets whose members are units of C(X). As rings of fractions these intermediate algebras inherit some algebraic properties from C* (X) but, in general, they are neither isomorphic to any C(T) nor even closed under composition. We characterize these two kinds of intermediate algebras by means of algebraic properties of the corresponding multiplicatively closed subsets, and we show that the intermediate algebras isomorphic to some C(T) are exactly those that are closed under inversion.

📜 SIMILAR VOLUMES

Intersections of maximal ideals in algeb
Intersections of maximal ideals in algebras between C∗(X) and C(X)
✍ Jesús M. Domı́nguez; J. Gómez Pérez 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 153 KB

Let C(X) be the algebra of all real-valued continuous functions on a completely regular space X, and C \* (X) the subalgebra of bounded functions. There is a known correspondence between a certain class of z-filters on X and proper ideals in C \* (X) that leads to theorems quite analogous to those f

Generalization of the B *-algebra (C0(X)
Generalization of the B *-algebra (C0(X),∥ ∥∞)
✍ Jorma Arhippainen; Jukka Kauppi 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 158 KB

## Abstract We give a generalization of the Stone–Weierstrass property for subalgebras of __C__ (__X__), with __X__ a completely regular Hausdorff space. In particular, we study in this paper some subalgebras of __C__~0~(__X__), with __X__ a locally compact Hausdorff space, provided with weighted n

On solutions of the matrix equations X−A
On solutions of the matrix equations X−AXB=C and X−AXB=C
✍ Tongsong Jiang; Musheng Wei 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 99 KB

This paper studies the solutions of complex matrix equations X -AXB = C and X -AXB = C, and obtains explicit solutions of the equations by the method of characteristic polynomial and a method of real representation of a complex matrix respectively.