Non-regularity for Banach function algebras

Feinstein, J.; Somerset, D.

Studia Mathematica, Tome 141 (2000), p. 53-68 / Harvested from The Polish Digital Mathematics Library

Résumé

Let A be a unital Banach function algebra with character space $Φ_{A}$ . For $x \in Φ_{A}$ , let $M_{x}$ and $J_{x}$ be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of $J_{x}$ is connected, and that if x does not belong to the Shilov boundary of A then the set $y \in Φ_{A} : M_{x} \supseteq J_{y}$ has an infinite connected subset. Various related results are given.

Publié le : 2000-01-01

Zbl 0976.46036

EUDML-ID : urn:eudml:doc:216773

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     author = {J. Feinstein and D. Somerset},
     title = {Non-regularity for Banach function algebras},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {53-68},
     zbl = {0976.46036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv141i1p53bwm}
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Feinstein, J.; Somerset, D. Non-regularity for Banach function algebras. Studia Mathematica, Tome 141 (2000) pp. 53-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv141i1p53bwm/

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