Real Banach Algebras. II.
L. Andrew Campbell, Norman L. Alling (1972)
Mathematische Zeitschrift
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L. Andrew Campbell, Norman L. Alling (1972)
Mathematische Zeitschrift
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Donald Z. Spicer (1973)
Colloquium Mathematicae
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V. Rakočević (1984)
Matematički Vesnik
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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...
Antonio Fernández López, Eulalia García Rus (1986)
Extracta Mathematicae
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A. Blanco (2010)
Studia Mathematica
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We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.
R.S. Doran, Wayne Tiller (1988)
Manuscripta mathematica
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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.
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.
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...
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.
H. Dales, F. Ghahramani, N. Grønbæek (1998)
Studia Mathematica
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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space is zero; i.e., . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable;...
Wong, Pak-Ken (1994)
International Journal of Mathematics and Mathematical Sciences
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H. G. Dales, A. Ülger (2015)
Studia Mathematica
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In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to...
C. J. Read (2005)
Studia Mathematica
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It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed...
Jon Froemke (1974)
Mathematische Zeitschrift
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J. Alaminos, R. Payá, A. R. Villena (2003)
Studia Mathematica
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We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.