Displaying similar documents to “Sectional representation of Banach modules and their multipliers.”

Gelfand representation of Banach modules

Joseph W. Kitchen, David A. Robbins

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PrefaceLet A be a commutative Banach algebra with maximal ideal space ∆ and let ^: A → C₀(∆) be the Gelfand representation of A. If M is a Banach module over A, then a bounded linear map φ: M → M₀, will be called a representation of M of Gelfund type if M₀ is a Banach module over C₀(∆) and φ is ^-linear in the sense that φ(ax) = âφ(x) for all a ∈ A and x ∈ M. Two such representations have been studied previously. In [50] and [51] Robbins describes such a representation in which M₀, is...

Bundles of Banach algebras.

Kitchen, J.W., Robbins, D.A. (1994)

International Journal of Mathematics and Mathematical Sciences

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Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani, Sima Soltani Renani (2011)

Studia Mathematica

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Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Weak amenability for the second dual of Banach modules

Fatemeh Anousheh, Davood Ebrahimi Bagha, Abasalt Bodaghi (2015)

Open Mathematics

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Let A be a Banach algebra, E be a Banach A-bimodule and Δ E → A be a bounded Banach A-bimodule homomorphism. It is shown that under some mild conditions, the weakΔ''-amenability of E'' (as an A''-bimodule) necessitates weak Δ-amenability of E (as an A-bimodule). Some examples of weak-amenable Banach modules are provided as well.