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Displaying similar documents to “Concerning a problem of Arens on removable ideals in Banach algebras”

Ideals and hereditary subalgebras in operator algebras

Melahat Almus, David P. Blecher, Charles John Read (2012)

Studia Mathematica

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This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently...

Generators of maximal left ideals in Banach algebras

H. G. Dales, W. Żelazko (2012)

Studia Mathematica

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In 1971, Grauert and Remmert proved that a commutative, complex, Noetherian Banach algebra is necessarily finite-dimensional. More precisely, they proved that a commutative, complex Banach algebra has finite dimension over ℂ whenever all the closed ideals in the algebra are (algebraically) finitely generated. In 1974, Sinclair and Tullo obtained a non-commutative version of this result. In 1978, Ferreira and Tomassini improved the result of Grauert and Remmert by showing that...

A characterization of Q-algebras of type F

W. Żelazko (2004)

Studia Mathematica

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We prove that a real or complex unital F-algebra is a Q-algebra if and only if all its maximal one-sided ideals are closed.

An isomorphism problem for algebras defined by some quivers and nonadmissible ideals

Stanisław Kasjan, Maja Sędłak (2008)

Colloquium Mathematicae

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Given a quiver Q, a field K and two (not necessarily admissible) ideals I, I' in the path algebra KQ, we study the problem when the factor algebras KQ/I and KQ/I' of KQ are isomorphic. Sufficient conditions are given in case Q is a tree extension of a cycle.

Complicated BE-algebras and characterizations of ideals

Yılmaz Çeven, Zekiye Çiloğlu (2015)

Discussiones Mathematicae - General Algebra and Applications

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In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive and complicated BE-algebra, characterizations of ideals are obtained.

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.