Isomorphisms of AC(σ) spaces

• Autorzy: Ian Doust , Michael Leinert
• Języki publikacji: EN

Abstrakty

EN

Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 26B30: Absolutely continuous functions, functions of bounded variation
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 228
• Numer: 1
• Strony: 7-31

Daty

wydano

2015

Twórcy

autor

Ian Doust

• School of Mathematics and Statistics, University of New South Wales, Sydney 2052 Australia

autor

Michael Leinert

• Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany

Identyfikatory

DOI

10.4064/sm228-1-3