𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Šilov boundaries for subspaces of continuous functions

✍ Scribed by Jesus Araujo; Juan J. Font

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

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we prove that if A is a strongly separating linear subspace of Ca(X). that is, for every x, y E X there exists f E A such that If(x)l ~ If(!t)l, then the Silov boundary for A exists and is the closure of the Choquet boundary, for A+ If, in addition, we assume that A is a closed subalgebra, then we p~ovide a proof of the following: the strong boundary points tbr A (r, eak points when X satisfies the first axiom of countability) are dense in the Silov boundary. Indeed they are a boundary for A. Our proof does not depend on the analogous results for sep'~ating closed subalgebras of C(X) (X compact) which contain the constant functions, that is, uniform algebras.

📜 SIMILAR VOLUMES

Bilinear isometries on subspaces of cont
Bilinear isometries on subspaces of continuous functions
✍ Juan J. Font; M. Sanchis 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 99 KB

Bilinear isometry, subspaces of continuous functions, generalized peak point ## MSC (2000) 46A55, 46E15 Let A and B be strongly separating linear subspaces of C0(X) and C0(Y ), respectively, and assume that ∂A = ∅ (∂A stands for the set of generalized peak points for A) and ∂B = ∅. Let T : A × B

On the extendibility of continuous funct
On the extendibility of continuous functions
✍ Horst Herrlich 📂 Article 📅 1974 🏛 Elsevier Science ⚖ 339 KB

nearness preserving maps extension of (uniformly) continluou s maps J Every uniformly continuous function from a dense subspace of a unifom space into a complete uniform space has a u.ni:~ormly continuou,s extension. This well-known theorem ka:: no direct topological counterpart. The reason becomes