A characteristic property of the algebra .
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Karakhanyan, M.I., Khor'kova, T.A. (2009)
Sibirskij Matematicheskij Zhurnal
Alonso Takahashi (1979)
Revista colombiana de matematicas
Mewomo, O.T., Akinbo, G. (2011)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Bodaghi, A., Eshaghi Gordji, M., Medghalchi, A.R. (2008)
Banach Journal of Mathematical Analysis [electronic only]
Abasalt Bodaghi, Behrouz Shojaee (2014)
Mathematica Bohemica
In the current work, a new notion of -weak amenability of Banach algebras using homomorphisms, namely --weak amenability is introduced. Among many other things, some relations between --weak amenability of a Banach algebra and , the Banach algebra of matrices with entries from , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra is ()--weakly amenable for any...
M. J. Heath (2005)
Studia Mathematica
In [6] J. F. Feinstein constructed a compact plane set X such that R(X), the uniform closure of the algebra of rational functions with poles off X, has no non-zero, bounded point derivations but is not weakly amenable. In the same paper he gave an example of a separable uniform algebra A such that every point in the character space of A is a peak point but A is not weakly amenable. We show that it is possible to modify the construction in order to produce examples which are also regular.
Bernardes, Nilson C.jun. (1996)
International Journal of Mathematics and Mathematical Sciences
Jitka Křížková, Pavla Vrbová (1974)
Commentationes Mathematicae Universitatis Carolinae
H. Seferoğlu (2003)
Studia Mathematica
Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then for each measure μ in reg(M(G)), where denotes the operator in B(X) defined by , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all...
Park, Choonkil, An, Jong Su, Moradlou, Fridoun (2008)
Journal of Inequalities and Applications [electronic only]
Manuilov, V.M. (1996)
Acta Mathematica Universitatis Comenianae. New Series
L. Oubbi (1995)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
U. Haagerup (1983)
Inventiones mathematicae
Rupert Lasser (2007)
Studia Mathematica
We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.
J. Duncan, A.L.T. Paterson (1990)
Mathematica Scandinavica
V. Runde (2001)
Studia Mathematica
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 an amenable...
Nico Spronk (2010)
Banach Center Publications
Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...
Seytek Tabaldyev (2014)
Open Mathematics
Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .
Alistair Bird (2010)
Banach Center Publications
The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.
Kyriazis, Athanasios (1989)
Portugaliae mathematica
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