Weak amenability for the second dual of Banach modules

Fatemeh Anousheh; Davood Ebrahimi Bagha; Abasalt Bodaghi

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Displaying similar documents to “Weak amenability for the second dual of Banach modules”

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.

3-Weak amenability of (2n)th duals of Banach algebras

Mina Ettefagh (2012)

Colloquium Mathematicae

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We show that under some conditions, 3-weak amenability of the (2n)th dual of a Banach algebra A for some n ≥ 1 implies 3-weak amenability of A.

Constructions preserving $n$ -weak amenability of Banach algebras

A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)

Mathematica Bohemica

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A surjective bounded homomorphism fails to preserve $n$ -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

Module structures on iterated duals of Banach algebras.

Bodaghi, A., Ettefagh, M., Eshaghi Gordji, M., Medghalchi, A.R. (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2015)

Annales UMCS, Mathematica

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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (Xν) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach-Saks property, then the deviation from the weak Banach-Saks property of an operator of a certain class between direct sums E(Xν) is equal to the supremum of such deviations attained on the coordinates Xν. This is a quantitative version for operators of...

M-structure and the Banach-Stone theorem

Ehrhard Behrends, Ursula Schmidt-Bichler (1981)

Studia Mathematica

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An extension of Helson-Edwards theorem to Banach modules.

Takahasi, Sin-Ei (1991)

International Journal of Mathematics and Mathematical Sciences

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On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

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We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (Xv) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(Xv) is equal to the supremum of such deviations attained on the coordinates Xv. This is a quantitative version for operators of...

A generalization of the weak amenability of Banach algebras.

Bodaghi, A., Eshaghi Gordji, M., Medghalchi, A.R. (2008)

Banach Journal of Mathematical Analysis [electronic only]

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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...

The structure of a subclass of amenable Banach algebras.

El Harti, R. (2004)

International Journal of Mathematics and Mathematical Sciences

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On the projectivity and flatness of some group modules

Gerhard Racher (2010)

Banach Center Publications

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In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.

A generalization of the $n$ -weak amenability of Banach algebras.

Mewomo, O.T., Akinbo, G. (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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An extension property for Banach spaces

Walden Freedman (2002)

Colloquium Mathematicae

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A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips...