A spectral synthesis property for $C_b(X,)$

H. Arizmendi-Peimbert, A. Carrillo-Hoyo, and A. Garcı́a. "A spectral synthesis property for $C_b(X, )$." Commentationes Mathematicae 48.2 (2008): null. <http://eudml.org/doc/291673>.

@article{H2008,
abstract = {Let $(C_b (X) , )$ be the algebra of all continuous bounded real or complex valued functions defined on a completely regular Hausdorff space $X$ with the usual algebraic operations and with the strict topology $$. It is proved that $(C_b (X) , )$ has a spectral synthesis, i.e. every of its closed ideals is an intersection of closed maximal ideals of codimension 1. We give one necessary and two sufficient conditions over $X$ in order that $(C_b (X) , )$ has no proper non-zero closed principal ideals. Moreover if $X$ satisfy any of these two conditions and is also a k-space, then any non zero element of $C_b(X)$ is invertible or a topological divisor of zero.},
author = {H. Arizmendi-Peimbert, A. Carrillo-Hoyo, A. Garcı́a},
journal = {Commentationes Mathematicae},
keywords = {spectral synthesis; strict topology; closed ideals; topological divisors of zero},
language = {eng},
number = {2},
pages = {null},
title = {A spectral synthesis property for $C_b(X, )$},
url = {http://eudml.org/doc/291673},
volume = {48},
year = {2008},
}

TY - JOUR
AU - H. Arizmendi-Peimbert
AU - A. Carrillo-Hoyo
AU - A. Garcı́a
TI - A spectral synthesis property for $C_b(X, )$
JO - Commentationes Mathematicae
PY - 2008
VL - 48
IS - 2
SP - null
AB - Let $(C_b (X) , )$ be the algebra of all continuous bounded real or complex valued functions defined on a completely regular Hausdorff space $X$ with the usual algebraic operations and with the strict topology $$. It is proved that $(C_b (X) , )$ has a spectral synthesis, i.e. every of its closed ideals is an intersection of closed maximal ideals of codimension 1. We give one necessary and two sufficient conditions over $X$ in order that $(C_b (X) , )$ has no proper non-zero closed principal ideals. Moreover if $X$ satisfy any of these two conditions and is also a k-space, then any non zero element of $C_b(X)$ is invertible or a topological divisor of zero.
LA - eng
KW - spectral synthesis; strict topology; closed ideals; topological divisors of zero
UR - http://eudml.org/doc/291673
ER -