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In the current work, a new notion of $n$ -weak amenability of Banach algebras using homomorphisms, namely $(ϕ, ψ)$ - $n$ -weak amenability is introduced. Among many other things, some relations between $(ϕ, ψ)$ - $n$ -weak amenability of a Banach algebra $𝒜$ and $M_{m} (𝒜)$ , the Banach algebra of $m \times m$ matrices with entries from $𝒜$ , 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 $L^{1} (G)$ is ( $ϕ, ψ$ )- $n$ -weakly amenable for any...

A Künneth formula in topological homology and its applications to the simplicial cohomology of $ℓ ¹ (ℤ ₊^{k})$

F. Gourdeau, Z. A. Lykova, M. C. White (2005)

Studia Mathematica

We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly...

A properly infinite Banach *-algebra with a non-zero, bounded trace

H. G. Dales, Niels Jakob Laustsen, Charles J. Read (2003)

Studia Mathematica

A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.

Algebra Involutions on the Bidual of a Banach Algebra.

Michael Grosser (1984)

Manuscripta mathematica

Algèbres de Fourier associées à une algèbre de Kac.

Jean de Cannière, Michel Enock, Jean-Marie Schwartz (1979)

Mathematische Annalen

Algèbres $L^{1}$ $p$ -adiques

Jean Fresnel, Bernard De Mathan (1978)

Bulletin de la Société Mathématique de France

Amenability and the second dual of a Banach algebra

Frédéric Gourdeau (1997)

Studia Mathematica

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.

Amenability of Banach and C*-algebras on locally compact groups

A. Lau, R. Loy, G. Willis (1996)

Studia Mathematica

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.

Amenability of Convolution Algebras.

A.T.-M. Lau, R.J. Loy (1996)

Mathematica Scandinavica

An application of Grothendieck's inequality to a problem in harmonic analysis

S. Kaijser (1975/1976)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

An example of a generalized completely continuous representation of a locally compact group

Detlev Poguntke (1993)

Studia Mathematica

There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image $π (L^{1} (G))$ of the $L^{1}$ -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.

Analytic functions and linearly ordered groups

I. Hirschman (1972)

Studia Mathematica

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A = ℓ^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras $ℓ^{p} (ω)$ .

Approximate amenability of semigroup algebras and Segal algebras [Book]

H. G. Dales, R. J. Loy (2010)

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