Geodesic
On dense ideals of $C^\ast $-algebras and generalizations of the Gelfand–Naimark Theorem
Jorma Arhippainen1 ; Jukka Kauppi1
1Department of Mathematical Sciences University of Oulu P.O. Box 3000 SF 90014 Oulun yliopisto, Finland
Studia Mathematica, Tome 215 (2013) no. 1, pp. 71-98
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We develop the theory of Segal algebras of commutative $C^\ast $-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand–Naimark Theorem. As an application, we describe faithful principal ideals of $C^\ast $-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.
DOI : 10.4064/sm215-1-5
Keywords: develop theory segal algebras commutative ast algebras emphasis functional representation main results extend gelfand naimark theorem application describe faithful principal ideals ast algebras key ingredient approach nachbin algebras generalize gelfand representation theory

Jorma Arhippainen  1   ; Jukka Kauppi  1

1 Department of Mathematical Sciences University of Oulu P.O. Box 3000 SF 90014 Oulun yliopisto, Finland 
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 generalizations of the Gelfand–Naimark Theorem
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 generalizations of the Gelfand–Naimark Theorem
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Jorma Arhippainen; Jukka Kauppi. On dense ideals of $C^\ast $-algebras and
 generalizations of the Gelfand–Naimark Theorem. Studia Mathematica, Tome 215 (2013) no. 1, pp. 71-98. doi: 10.4064/sm215-1-5

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