Functiones et Approximatio Commentarii Mathematici

Concerning dense subideals in commutative Banach algebras

Wiesław Żelazko

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Abstract

In the paper [2] we have shown that in the case of a separable Banach algebra $A$ the necessary and sufficient condition in order that a closed ideal $I\subset A$ has a dense subideal is that $I$ is not finitely (algebraically) generated. We conjectured that this result is true in the general case. In this paper we give an example showing that this conjecture fails to be true.

Article information

Source
Funct. Approx. Comment. Math., Volume 48, Number 1 (2013), 113-115.

Dates
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1364222832

Digital Object Identifier
doi:10.7169/facm/2013.48.1.8

Mathematical Reviews number (MathSciNet)
MR3086963

Zentralblatt MATH identifier
1275.46037

Subjects
Primary: 46J20: Ideals, maximal ideals, boundaries

Keywords
commutative Banach algebras dense subideals the first uncountable ordinal

Citation

Żelazko, Wiesław. Concerning dense subideals in commutative Banach algebras. Funct. Approx. Comment. Math. 48 (2013), no. 1, 113--115. doi:10.7169/facm/2013.48.1.8. https://projecteuclid.org/euclid.facm/1364222832


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References

  • H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, Berlin 1971.
  • W. Żelazko, When does a closed ideal of a commutative unital Banach algebra contain a dense subideal?, Funct. Approx. Comment. Math. 44 (2011), 285–287.