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Some notions of amenability for certain products of Banach algebras

Eghbal Ghaderi, Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

For two Banach algebras and ℬ, an interesting product × θ ℬ , called the θ-Lau product, was recently introduced and studied for some nonzero characters θ on ℬ. Here, we characterize some notions of amenability as approximate amenability, essential amenability, n-weak amenability and cyclic amenability between and ℬ and their θ-Lau product.

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

Zhiguo Hu (1998)

Studia Mathematica

Let A be a semisimple commutative regular tauberian Banach algebra with spectrum Σ A . In this paper, we study the norm spectra of elements of s p a n ¯ Σ A and present some applications. In particular, we characterize the discreteness of Σ A in terms of norm spectra. The algebra A is said to have property (S) if, for all φ ∈ ¯ Σ A 0 , φ has a nonempty norm spectrum. For a locally compact group G, let ℳ 2 d ( Ĝ ) denote the C*-algebra generated by left translation operators on L 2 ( G ) and G d denote the discrete group G. We prove that the Fourier...

Sur un problème de I. Glicksberg : les idéaux fermés de type fini de M ( G )

Bernard Host, François Parreau (1978)

Annales de l'institut Fourier

Soit μ ∈ M ( G ) , algèbre de convolution des mesures de Radon bornées sur le groupe abélien localement compact G . Pour que μ * M ( G ) soit fermé dans M ( G ) (ou, ce qui revient au même, pour que μ * L 1 ( G ) soit fermé), il faut et il suffit que μ soit la convolution d’une mesure inversible et d’une mesure idempotente.

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