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On duals of Calderón-Lozanovskiĭ intermediate spaces

100%

Raynaud Y.

Studia Mathematica

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1997

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tom 124

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nr 1

9-36

EN

We give a description of the dual of a Calderón-Lozanovskiĭ intermediate space φ(X,Y) of a couple of Banach Köthe function spaces as an intermediate space ψ(X*,Y*) of the duals, associated with a "variable" function ψ.

2

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Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

63%

Henson C. W., Raynaud Y.

Commentationes Mathematicae

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2016

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tom 56

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nr 1

EN

We give a criterion ensuring that the elementary class of a modular Banach space $E$ (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of $E$) consists of all direct sums $E\oplus_m H$, where $H$ is an arbitrary Hilbert space and $\oplus_m$ denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.

3

Dual spaces to Orlicz-Lorentz spaces

51%

Kamińska A., Leśnik K., Raynaud Y.

Studia Mathematica

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2014

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tom 222

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nr 3

229-261

EN

For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space $Λ_{φ,w}$ or the sequence space $λ_{φ,w}$, equipped with either the Luxemburg or Amemiya norms. The first description is via the modular $inf{∫ φ⁎(f*/|g|)|g|: g ≺ w}$, where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular $∫_{I} φ⁎((f*)⁰/w)w$,where (f*)⁰ is Halperin's level function of f* with respect to w. That these two descriptions are equivalent results from the identity $inf{ ∫ ψ(f*/|g|)|g|: g ≺ w} = ∫_{I} ψ((f*)⁰/w)w$, valid for any measurable function f and any Orlicz function ψ. An analogous identity and dual representations are also presented for sequence spaces.

Ograniczanie wyników

2 Studia Mathematica

1 Commentationes Mathematicae

3 Raynaud Y.

1 Henson C. W.

1 Kamińska A.

1 Leśnik K.

1 2016

1 2014

1 1997

On duals of Calderón-Lozanovskiĭ intermediate spaces

Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

Dual spaces to Orlicz-Lorentz spaces