Continuity of Jordan homomorphisms of Banach algebras.
Dumitru D. Draghia (1995)
Extracta Mathematicae
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Dumitru D. Draghia (1995)
Extracta Mathematicae
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Volker Runde (1993)
Studia Mathematica
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Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes...
Gerard Murphy (1994)
Banach Center Publications
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We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.
Dumitru D. Draghia (1995)
Extracta Mathematicae
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J. Vukman (1988)
Aequationes mathematicae
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Donald Z. Spicer (1973)
Colloquium Mathematicae
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A. Jabbari, T. Mehdi Abad, M. Zaman Abadi (2011)
Colloquium Mathematicae
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Generalizing the concept of inner amenability for Lau algebras, we define and study the notion of φ-inner amenability of any Banach algebra A, where φ is a homomorphism from A onto ℂ. Several characterizations of φ-inner amenable Banach algebras are given.
R. Kantrowitz, Michael M. Neumann (1995)
Czechoslovak Mathematical Journal
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Niels Groenbaek (1989)
Studia Mathematica
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Abdullah H. Al-Moajil (1980/81)
Manuscripta mathematica
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Tsiu-Kwen Lee, Cheng-Kai Liu (2009)
Studia Mathematica
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Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies...
V. Runde (2001)
Studia Mathematica
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We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions...
Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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Yong Zhang (2010)
Banach Center Publications
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We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.