Polynomially compact elements of Banach algebras
V. Rakočević (1984)
Matematički Vesnik
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V. Rakočević (1984)
Matematički Vesnik
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Donald Z. Spicer (1973)
Colloquium Mathematicae
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Graham Allan, Allan Sinclair (1976)
Studia Mathematica
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Antonio Fernández López, Eulalia García Rus (1986)
Extracta Mathematicae
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Niels Gronbaek (1982)
Mathematica Scandinavica
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Bertram Yood (2008)
Studia Mathematica
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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.
Uygul, Faruk (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Rasoul Nasr-Isfahani, Sima Soltani Renani (2011)
Studia Mathematica
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Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.
Matthew Daws (2007)
Studia Mathematica
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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...
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...
Vladimír Müller (1988)
Studia Mathematica
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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.
Jitka Křížková, Pavla Vrbová (1974)
Commentationes Mathematicae Universitatis Carolinae
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