Czasopismo
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Języki publikacji
Abstrakty
We continue the study of the completeness and completions of normed algebras of differentiable functions Dⁿ(K) (where K is a perfect, compact plane set), initiated by Bland, Dales and Feinstein [Studia Math. 170 (2005) and Indian J. Pure Appl. Math. 41 (2010)]. We prove new characterizations of the completeness of D¹(K) and results concerning the semisimplicity of the completion of D¹(K). In particular, we prove that semi-rectifiability is necessary for the completion of D¹(K) to be semisimple in the case where K lies on a rectifiable, injective curve. Furthermore, we answer a question posed by Dales and Feinstein and show that another question posed by them has an affirmative answer in some special cases. As compared with the approach taken by Bland, Dales and Feinstein, which comes from the theory of function algebras, we move within an operator-theoretic framework by investigating the mapping properties of certain derivation operators.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
19-45
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Department of Mathematics, Institute of Analysis, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-2