Fixed point characterization of left amenable Lau algebras.
Nasr-Isfahani, R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Nasr-Isfahani, R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Anthony To-Ming Lau (1983)
Fundamenta Mathematicae
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Ross Stokke (2004)
Studia Mathematica
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We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally...
A. Lau, R. Loy, G. Willis (1996)
Studia Mathematica
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Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.
Frédéric Gourdeau (1997)
Studia Mathematica
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Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.
Michael Yin-Hei Cheng (2012)
Studia Mathematica
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Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.
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.
A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)
Mathematica Bohemica
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A surjective bounded homomorphism fails to preserve -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
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...
H. G. Dales, R. J. Loy
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In recent years, there have been several studies of various ’approximate’ versions of the key notion of amenability, which is defined for all Banach algebras; these studies began with work of Ghahramani and Loy in 2004. The present memoir continues such work: we shall define various notions of approximate amenability, and we shall discuss and extend the known background, which considers the relationships between different versions of approximate amenability. There are a number of open...
Masiha, Hashem (2008)
International Journal of Mathematics and Mathematical Sciences
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Fereidoun Ghahramani, Anthony To-Ming Lau (2005)
Studia Mathematica
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We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.