On ideals consisting of topological zero divisors

Antoni Wawrzyńczyk

Studia Mathematica (2000)

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

Abstract

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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.

How to cite

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Wawrzyńczyk, 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

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

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