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Generalization of the topological algebra $(C_{b} (X), β)$

Jorma Arhippainen; Jukka Kauppi — 2009

Studia Mathematica

We study subalgebras of $C_{b} (X)$ equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.

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

Jorma Arhippainen; Jukka 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 Abel; Jorma Arhippainen; Jukka 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 $S \in 𝔖$ . 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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Currently displaying 1 – 3 of 3

Generalization of the topological algebra ( C b ( X ) , β )

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

Description of quotient algebras in function algebras containing continuous unbounded functions

Generalization of the topological algebra $(C_{b} (X), β)$