Complicated BE-algebras and characterizations of ideals

Yılmaz Çeven; Zekiye Çiloğlu

Displaying similar documents to “Complicated BE-algebras and characterizations of ideals”

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

Jorma Arhippainen, Jukka Kauppi (2013)

Studia Mathematica

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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.

Topological algebras in which all maximal two-sided ideals are closed

Mati Abel, Krzysztof Jarosz (2005)

Banach Center Publications

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We characterize unital topological algebras in which all maximal two-sided ideals are closed.

Korovkin theory in normed algebras

Ferdinand Beckhoff (1991)

Studia Mathematica

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If A is a normed power-associative complex algebra such that the selfadjoint part is normally ordered with respect to some order, then the Korovkin closure (see the introduction for definitions) of T ∪ {t* ∘ t| t ∈ T} contains J*(T) for any subset T of A. This can be applied to C*-algebras, minimal norm ideals on a Hilbert space, and to H*-algebras. For bounded H*-algebras and dual C*-algebras there is even equality. This answers a question posed in [1].