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Displaying similar documents to “On embeddings of C₀(K) spaces into C₀(L,X) spaces”

How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?

Leandro Candido, Elói Medina Galego (2012)

Fundamenta Mathematicae

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For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...

On positive embeddings of C(K) spaces

Grzegorz Plebanek (2013)

Studia Mathematica

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We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such...

Banach-Mackey spaces.

Qiu, Jing Hui, McKennon, Kelly (1991)

International Journal of Mathematics and Mathematical Sciences

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Note on quasi-bounded sets.

Bosch, Carlos, Kučera, Jan, McKennon, Kelly (1991)

International Journal of Mathematics and Mathematical Sciences

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Isomorphisms of AC(σ) spaces

Ian Doust, Michael Leinert (2015)

Studia Mathematica

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Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple...

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.