On finite-dimensional normed spaces over 𝐶_{𝑝}

Kubzdela, Albert

doi:10.1090/conm/384/07135

Cited by 5 publications

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“…If K is non-spherically complete, then E u does not contain an isometric image of any non-archimedean Banach spaces of countable type. Indeed, in this case there exists finite-dimensional normed spaces without orthogonal bases, see [11,Example 2.3.26] and [6]. Take E = K 2 v , where K 2 v is a two-dimensional normed space over K without two non-zero orthogonal elements, and assume that there exists an isometric embedding i : E → E u .…”

Section: Non-archimedean Banach Space Of Universal Disposition For Fi...mentioning

confidence: 99%

On non-archimedean Gurarii spaces

Kcakol,

Kubiś,

Kubzdela

2016

Preprint

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Let U F N A be the class of all non-archimedean finite-dimensional Banach spaces. A non-archimedean Gurari ǐ Banach space G over a non-archimedean valued field K is constructed, i.e. a non-archimedean Banach space G of countable type which is of almost universal disposition for the class U F N A . This means: for every isometry g : X → Y , where Y ∈ U F N A and X is a subspace of G, and every ε ∈ (0, 1) there exists an ε-isometry f : Y → G such that f (g(x)) = x for all x ∈ X. We show that all non-archimedean Banach spaces of almost universal disposition for the class U F N A are ε-isometric. Furthermore, all non-archimedean Banach spaces of almost universal disposition for the class U F N A are isometrically isomorphic if and only if K is spherically complete and {|λ| : λ ∈ K\ {0}} = (0, ∞).

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Section: Non-archimedean Banach Space Of Universal Disposition For Fi...mentioning

confidence: 99%

On non-archimedean Gurarii spaces

Kcakol,

Kubiś,

Kubzdela

2016

Preprint

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“…If K is spherically complete, every finite-dimensional space has an orthogonal base (Theorem 2.1), so E has the FDDP if and only if E has an orthogonal base. However, if K is not spherically complete there exist various kinds of finite-dimensional spaces without orthogonal base (see [6]); for these K the class of Banach spaces with the FDDP can be viewed as a natural proper generalization of the class of Banach spaces with an orthogonal base.…”

Section: Preliminariesmentioning

confidence: 99%

The metric approximation property in non-archimedean normed spaces

Pérez-García¹,

Schikhof²

2014

Glas. Mat. Ser. III

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Abstract. A normed space E over a rank 1 non-archimedean valued field K has the metric approximation property (MAP) if the identity on E can be approximated pointwise by finite rank operators of norm 1.Characterizations and hereditary properties of the MAP are obtained. For Banach spaces E of countable type the following main result is derived: E has the MAP if and only if E is the orthogonal direct sum of finitedimensional spaces (Theorem 4.9). Examples of the MAP are also given. Among them, Example 3.3 provides a solution to the following problem, posed by the first author in [8, 4.5]. Does every Banach space of countable type over K have the MAP?

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The finite-dimensional decomposition property in non-Archimedean Banach spaces

Kubzdela

Pérez-García

2014

Acta. Math. Sin.-English Ser.

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On finite-dimensional normed spaces over 𝐶_{𝑝}

Cited by 5 publications

References 0 publications

On non-archimedean Gurarii spaces

On non-archimedean Gurarii spaces

The metric approximation property in non-archimedean normed spaces

The finite-dimensional decomposition property in non-Archimedean Banach spaces

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