Closed ideals in topological algebras: a characterization of the topological Φ -algebra C k ( X )

F. Montalvo; Antonio A. Pulgarín; Batildo Requejo Fernández

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 903-918
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Montalvo, F., Pulgarín, Antonio A., and Requejo Fernández, Batildo. "Closed ideals in topological algebras: a characterization of the topological $\Phi $-algebra $C_k(X)$." Czechoslovak Mathematical Journal 56.3 (2006): 903-918. <http://eudml.org/doc/31076>.

@article{Montalvo2006,
abstract = {Let $A$ be a uniformly closed and locally m-convex $\Phi $-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 $\Phi $-algebra of all the real continuous functions on a normal topological space $X$ endowed with the compact convergence topology.},
author = {Montalvo, F., Pulgarín, Antonio A., Requejo Fernández, Batildo},
journal = {Czechoslovak Mathematical Journal},
keywords = {locally m-convex algebra; $\Phi $-algebra; compact convergence topology; locally m-convex algebra; -algebra; compact convergence topology},
language = {eng},
number = {3},
pages = {903-918},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Closed ideals in topological algebras: a characterization of the topological $\Phi $-algebra $C_k(X)$},
url = {http://eudml.org/doc/31076},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Montalvo, F.
AU - Pulgarín, Antonio A.
AU - Requejo Fernández, Batildo
TI - Closed ideals in topological algebras: a characterization of the topological $\Phi $-algebra $C_k(X)$
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 903
EP - 918
AB - Let $A$ be a uniformly closed and locally m-convex $\Phi $-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 $\Phi $-algebra of all the real continuous functions on a normal topological space $X$ endowed with the compact convergence topology.
LA - eng
KW - locally m-convex algebra; $\Phi $-algebra; compact convergence topology; locally m-convex algebra; -algebra; compact convergence topology
UR - http://eudml.org/doc/31076
ER -

References

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