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2015•Unpublished venueRequires access

3-HOMOMORPHISM AMENABILITY OF BANACH ALGEBRAS

Abasalt Bodaghi, Malihe Peyvaste

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Abstract

In the current work, the notion of 3-homomorphism amenability of Banach algebras is introduced. The hereditary properties of this new concept for Banach algebras are investigated and the relations between 3-homomorphism amenability of a Banach algebra and its ideals are found. The equivalence of 3-homomorphism amenability and the concept of the (right) character amenability is proved. As a consequence, 3-homomorphism amenability for either of the group algebra L 1 (G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G.

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What this paper is about

In the current work, the notion of 3-homomorphism amenability of Banach algebras is introduced. The hereditary properties of this new concept for Banach algebras are investigated and the relations between 3-homomorphism amenability of a Banach algebra and its ideals are found. The equivalence of 3-homomorphism amenability and the concept of the (right) character amenability is proved. As a consequence, 3-homomorphism amenability for either of the group algebra L 1 (G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G.

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Available abstract

In the current work, the notion of 3-homomorphism amenability of Banach algebras is introduced. The hereditary properties of this new concept for Banach algebras are investigated and the relations between 3-homomorphism amenability of a Banach algebra and its ideals are found. The equivalence of 3-homomorphism amenability and the concept of the (right) character amenability is proved. As a consequence, 3-homomorphism amenability for either of the group algebra L 1 (G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G.

Key concepts: Homomorphism, Algebra homomorphism, Banach algebra, Mathematics, Pure mathematics, Equivalence (formal languages), Locally compact group, Algebra over a field

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