# On ideals consisting of topological zero divisors

Studia Mathematica (2000)

- Volume: 142, Issue: 3, page 245-251
- ISSN: 0039-3223

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topWawrzyńczyk, Antoni. "On ideals consisting of topological zero divisors." Studia Mathematica 142.3 (2000): 245-251. <http://eudml.org/doc/216801>.

@article{Wawrzyńczyk2000,

abstract = {The class ω(A) of ideals consisting of topological zero divisors of a commutative Banach algebra A is studied. We prove that the maximal ideals of the class ω(A) are of codimension one.},

author = {Wawrzyńczyk, Antoni},

journal = {Studia Mathematica},

keywords = {commutative Banach algebra; joint topological divisors; maximal ideal},

language = {eng},

number = {3},

pages = {245-251},

title = {On ideals consisting of topological zero divisors},

url = {http://eudml.org/doc/216801},

volume = {142},

year = {2000},

}

TY - JOUR

AU - Wawrzyńczyk, Antoni

TI - On ideals consisting of topological zero divisors

JO - Studia Mathematica

PY - 2000

VL - 142

IS - 3

SP - 245

EP - 251

AB - The class ω(A) of ideals consisting of topological zero divisors of a commutative Banach algebra A is studied. We prove that the maximal ideals of the class ω(A) are of codimension one.

LA - eng

KW - commutative Banach algebra; joint topological divisors; maximal ideal

UR - http://eudml.org/doc/216801

ER -

## References

top- [1] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dek- ker, 1988.
- [2] V. Müller, Removability of ideals in commutative Banach algebras, Studia Math. 78 (1984), 297-307. Zbl0495.46037
- [3] Z. Słodkowski, On ideals consisting of joint topological divisors of zero, Studia Math. 48 (1973), 83-88. Zbl0271.46046
- [4] W. Żelazko, A characterization of Shilov boundary in function algebras, Comment. Math. 14 (1970) 59-64.
- [5] W. Żelazko, On a certain class of non-removable ideals in Banach algebras, Studia Math. 44 (1972) 87-92. Zbl0213.40603
- [6] W. Żelazko, Banach Algebras, PWN-Elsevier, 1973.
- [7] W. Żelazko, An axiomatic approach to joint spectra I, Studia Math. 64 (1979) 249-261. Zbl0426.47002

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