Absolute continuity in the dual of a Banach algebra
Author:
Stephen Jay Berman
Journal:
Trans. Amer. Math. Soc. 243 (1978), 169194
MSC:
Primary 46H05; Secondary 46J05
MathSciNet review:
502901
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Abstract: If A is a Banach algebra, G is in the dual space , and I is a closed ideal in A, then let denote the norm of the restriction of G to I. We define a relation in as follows: if for every there exists a such that if I is a closed ideal in A and then . We explore this relation (which coincides with absolute continuity of measures when A is the algebra of continuous functions on a compact space) and related concepts in the context of several Banach algebras, particularly the algebra of differentiable functions and the algebra of continuous functions on the disc with holomorphic extensions to the interior. We also consider generalizations to noncommutative algebras and Banach modules.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197805029015
PII:
S 00029947(1978)05029015
Keywords:
Ideals in Banach algebras,
absolute continuity,
RadonNikodym theorems
Article copyright:
© Copyright 1978
American Mathematical Society
