Concerning a problem of Arens on removable ideals in Banach algebras
W. Żelazko (1974)
Colloquium Mathematicae
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W. Żelazko (1974)
Colloquium Mathematicae
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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.
David P. Blecher, Matthew Neal (2012)
Studia Mathematica
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We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in...
V. Losert, E. Kotzmann, H. Rindler (1979)
Mathematische Annalen
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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.
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.
Sterling K. Berberian (1983)
Mathematische Zeitschrift
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Wend Werner (1991)
Mathematische Annalen
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W. Żelazko (2005)
Studia Mathematica
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We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.
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.
M. Cabrera, Amir A. Mohammed (2003)
Studia Mathematica
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We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation...
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.
Karl Heinrich Hofmann, Francisco Javier Thayer
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CONTENTSIntroduction........................................................................................................................... 51. Finite-dimensional C*-algebras.................................................................................. 8 The objects...................................................................................................................... 8 The morphisms.................................................................................................................
Fidel Hernández Advíncula, Eduardo do Nascimento Marcos (2007)
Colloquium Mathematicae
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The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
Roh, Eun Hwan (2004)
International Journal of Mathematics and Mathematical Sciences
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Yngve Domar (1972)
Mathematische Zeitschrift
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Mohammed El Bachir Bekka (1984)
Mathematische Annalen
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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].
Juhani Nieminen (1978)
Colloquium Mathematicae
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C.M. Edwards, G.T. Rüttimann (1990)
Mathematische Zeitschrift
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J. Słomiński
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CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras..........................................................................................................................................................................