1972
DOI: 10.1112/plms/s3-25.2.329
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Embedding the Algebra of Formal Power Series in a Banach Algebra

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Cited by 49 publications
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“…It is easy to see that F is not a Banach algebra with respect to any norm, but it is certainly not obvious whether or not F is normable. But, in a significant break-through, this was shown to be the case by Graham Allan in 1972 [1]. This theorem is given as [6, Theorem 5.7.1]; it uses the algebraic extension methods of [6, §1.7] and an obvious 'framework map', namely n → a n , N → A, for a suitable element a in a Banach algebra A, and was an avatar for later embedding theorems.…”
Section: This Algebra Is Often Denoted By R[[x]]; Its Complex Versionmentioning
confidence: 99%
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“…It is easy to see that F is not a Banach algebra with respect to any norm, but it is certainly not obvious whether or not F is normable. But, in a significant break-through, this was shown to be the case by Graham Allan in 1972 [1]. This theorem is given as [6, Theorem 5.7.1]; it uses the algebraic extension methods of [6, §1.7] and an obvious 'framework map', namely n → a n , N → A, for a suitable element a in a Banach algebra A, and was an avatar for later embedding theorems.…”
Section: This Algebra Is Often Denoted By R[[x]]; Its Complex Versionmentioning
confidence: 99%
“…Allan noted in [1] that there are elements of finite closed descent in V , and hence that there is a unital embedding of F into V . It follows that F is normable.…”
Section: This Algebra Is Often Denoted By R[[x]]; Its Complex Versionmentioning
confidence: 99%
See 3 more Smart Citations