Normed algebras of differentiable functions on compact plane sets: completeness and semisimple completions

• Autorzy: Heiko Hoffmann
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 207
• Numer: 1
• Strony: 19-45

Daty

wydano

2011

Twórcy

autor

Heiko Hoffmann

• Department of Mathematics, Institute of Analysis, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany

Identyfikatory

DOI

10.4064/sm207-1-2