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On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

Jorma ArhippainenJukka Kauppi — 2013

Studia Mathematica

We develop the theory of Segal algebras of commutative C*-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*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.

Description of quotient algebras in function algebras containing continuous unbounded functions

Mati AbelJorma ArhippainenJukka Kauppi — 2012

Open Mathematics

Let X be a completely regular Hausdorff space, 𝔖 a cover of X, and C b ( X , 𝕂 ; 𝔖 ) the algebra of all 𝕂 -valued continuous functions on X which are bounded on every S 𝔖 . A description of quotient algebras of C b ( X , 𝕂 ; 𝔖 ) is given with respect to the topologies of uniform and strict convergence on the elements of 𝔖 .

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