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ON SUBSPECTRA GENERATED IN SUBALGEBRAS

Published online by Cambridge University Press:  12 May 2003

ANTONI WAWRZYŃCZYK
ANTONI WAWRZYŃCZYK
Affiliation:
Universidad Autónoma Metropolitana – Iztapalapa Departamento de Matemáticas, Av. San Rafael Atlixco 186, col. Vicentina, 09 340 México, D. F. AP 55-534 [email protected]
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Abstract

Let $B$ be a unital commutative Banach algebra, and let $A$ be an arbitrary subalgebra of $B$. Suppose that an ideal $I\subset A$ consists of elements that are non-invertible in $B$. Then there exists an ideal $J$ in $A$ that: (i) contains $I$, (ii) also consists of elements non-invertible in $B$, and (iii) is of codimension one in $A$. This result is used in the study of a class of subspectra on $A$.

Keywords

46J20
Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 3 , May 2003 , pp. 367 - 372
Copyright
© The London Mathematical Society 2003

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