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Generalization of the B *‐algebra ( C 0 ( X ),∥ ∥ ∞ )
Author(s) -
Arhippainen Jorma,
Kauppi Jukka
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610718
Subject(s) - hausdorff space , mathematics , generalization , norm (philosophy) , ideal (ethics) , locally compact space , paracompact space , space (punctuation) , compact space , pure mathematics , urysohn and completely hausdorff spaces , property (philosophy) , algebra over a field , discrete mathematics , hausdorff measure , mathematical analysis , hausdorff dimension , computer science , political science , philosophy , epistemology , law , operating system
We give a generalization of the Stone–Weierstrass property for subalgebras of C ( X ), with X a completely regular Hausdorff space. In particular, we study in this paper some subalgebras of C 0 ( X ), with X a locally compact Hausdorff space, provided with weighted norm topology. By using the Stone–Weierstrass property, we then describe the ideal structure of these algebras. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)