Maximal ideals in algebras of vector-valued functions.

Kitchen, J.W.; Robbins, D.A.

Displaying similar documents to “Maximal ideals in algebras of vector-valued functions.”

On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen (1992)

Studia Mathematica

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Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.

Description of quotient algebras in function algebras containing continuous unbounded functions

Mati Abel, Jorma Arhippainen, Jukka Kauppi (2012)

Open Mathematics

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Let X be a completely regular Hausdorff space, $𝔖$ a cover of X, and $C_{b} (X, 𝕂; 𝔖)$ the algebra of all $𝕂$ -valued continuous functions on X which are bounded on every $S \in 𝔖$ . A description of quotient algebras of $C_{b} (X, 𝕂; 𝔖)$ is given with respect to the topologies of uniform and strict convergence on the elements of $𝔖$ .

Finiteness properties of topological algebras, I

A. V. Ferreira, G. Tomassini (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou (1992)

Studia Mathematica

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A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

Bundles of Banach algebras.

Kitchen, J.W., Robbins, D.A. (1994)

International Journal of Mathematics and Mathematical Sciences

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Closed ideals in topological algebras: a characterization of the topological $Φ$ -algebra $C_{k} (X)$

F. Montalvo, Antonio A. Pulgarín, Batildo Requejo Fernández (2006)

Czechoslovak Mathematical Journal

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Let $A$ be a uniformly closed and locally m-convex $Φ$ -algebra. We obtain internal conditions on $A$ stated in terms of its closed ideals for $A$ to be isomorphic and homeomorphic to $C_{k} (X)$ , the $Φ$ -algebra of all the real continuous functions on a normal topological space $X$ endowed with the compact convergence topology.

A theorem concerning Ditkin's condition

Larsen, R. (1971)

Portugaliae mathematica

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Topologies of compact families on the ideal space of a Banach algebra

Ferdinand Beckhoff (1996)

Studia Mathematica

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Let be a family of compact sets in a Banach algebra A such that is stable with respect to finite unions and contains all finite sets. Then the sets $U (K) : = I \in I d (A) : I \cap K = \emptyset$ , K ∈ define a topology τ() on the space Id(A) of closed two-sided ideals of A. is called normal if $I_{i} \to I$ in (Id(A),τ()) and x ∈ A╲I imply $l i m i n f_{i} ∥ x + I_{i} ∥ > 0$ . (1) If the family of finite subsets of A is normal then Id(A) is locally compact in the hull kernel topology and if moreover A is separable then Id(A) is second countable. (2) If the family of countable...