On isomorphic classifications of spaces of compact operators

Galego, Elói Medina

doi:10.1090/s0002-9939-09-09828-1

Cited by 8 publications

(18 citation statements)

References 15 publications

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“…In contrast to the analogous results of [7], these new results need no additional hypothesis on the space X * . As a consequence, we generalize some results of [10]; see Propositions 2.13 and 3.2 and Lemma 3.1, which, in turn, will be useful in the proof of Theorem 1.1.…”

Section: Some Preliminary Resultsmentioning

confidence: 54%

“…In order to do this, we first prove Theorem 1.1, which is a refinement of [10,Theorem 1.1]. This result is an extension of the classical isomorphic classification of the R ξ spaces accomplished by Bessaga and Pe lczyński [1], in the case where …”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 94%

“…Therefore, Corollary 1.3 furnishes a complete isomorphic classification of the spaces K(R ξ , R η ), where ξ ≥ ω and η ≥ ω. The case ω ≤ ξ = η < ω 1 is due to C. Samuel [22], and the case ω ≤ ξ < ω 1 and η ≥ ω was obtained in [10] under the Continuum Hypothesis. Remark 1.5.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…The main goal of the present paper is to complete the partial isomorphic classifications of some Banach spaces of compact operators recently obtained in [10] and [22]. In order to do this, we first prove Theorem 1.1, which is a refinement of [10,Theorem 1.1].…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

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Complete isomorphic classifications of some spaces of compact operators

Galego¹

2009

Proc. Amer. Math. Soc.

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Abstract. This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal α and denoting by X ξ , ω α ≤ ξ < ω α+1 , the Banach space of all X-valued continuous functions defined in the interval of ordinals [0, ξ] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spacesIt is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases:1. X * contains no copy of c 0 and has the Mazur property, and Y = c 0 (J) for every set J.2. X = c 0 (I) and Y = l q (J) for any infinite sets I and J and 1 ≤ q < ∞. 3. X = l p (I) and Y = l q (J) for any infinite sets I and J and 1 ≤ q

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Section: Some Preliminary Resultsmentioning

confidence: 54%

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 94%

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

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Complete isomorphic classifications of some spaces of compact operators

Galego¹

2009

Proc. Amer. Math. Soc.

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“…Since |I| < α, by[11, Lemma 2.4] we infer that c 0 → X. 2We end this section by improving [12, Lemma 2.10].…”

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confidence: 93%

Spaces of compact operators on C(2m⊕[0,α]) spaces

Galego

2010

Journal of Mathematical Analysis and Applications

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We classify up to isomorphism the spaces of compact operators K(E, F ), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2 m ⊕ [0, α], the topological sum of Cantor cubes 2 m and the intervals of ordinal numbers [0, α]. More precisely, we prove that if 2 m and ℵ γ are not real-valued measurable cardinals and n ℵ 0 is not sequential cardinal, then for every ordinals ξ , η, λ and μ with ξ ω 1 , η ω 1 , λ = μ < ω or λ, μ ∈ [ω γ , ω γ +1 [, the following statements are equivalent:for some regular cardinal α and finite ordinalsThus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators.

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The C(K,X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

Galego

2011

Journal of Mathematical Analysis and Applications

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On isomorphic classifications of spaces of compact operators

Cited by 8 publications

References 15 publications

Complete isomorphic classifications of some spaces of compact operators

Complete isomorphic classifications of some spaces of compact operators

Spaces of compact operators on C(2m⊕[0,α]) spaces

The C(K,X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

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