## Functiones et Approximatio Commentarii Mathematici

### Concerning dense subideals in commutative Banach algebras

Wiesław Żelazko

#### 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

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

#### 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

#### 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.