Abstract
Let B be a unital commutative Banach algebra, and let A be an arbitrary subalgebra of B. Suppose that an ideal I ⊂ 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. 2000 Mathematics Subject Classification 46J20.
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