Wyniki wyszukiwania

1

Lattice structures in Orlicz spaces

100%

Hernández F.

Banach Center Publications

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2004

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tom 64

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nr 1

71-84

2

Disjoint strict singularity of inclusions between rearrangement invariant spaces

51%

Hernández F., Sánchez V., Semenov E.

Studia Mathematica

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2001

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tom 144

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nr 3

209-226

EN

It is studied when inclusions between rearrangement invariant function spaces on the interval [0,∞) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions $L¹ ∩ L^{∞} ↪ E$ and $E ↪ L¹ + L^{∞}$ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.

3

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

51%

Astashkin S., Hernández F., Semenov E.

Studia Mathematica

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2009

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tom 193

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nr 3

269-283

EN

If G is the closure of $L_{∞}$ in exp L₂, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular and E ⊊ G. For any Marcinkiewicz space M(φ) ⊂ G such that M(φ) is not an interpolation space between $L_{∞}$ and G it is proved that there exists another Marcinkiewicz space M(ψ) ⊊ M(φ) with the property that the M(ψ) and M(φ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.

Ograniczanie wyników

2 Studia Mathematica

1 Banach Center Publications

3 Hernández F.

2 Semenov E.

1 Astashkin S.

1 Sánchez V.

1 2009

1 2004

1 2001

Lattice structures in Orlicz spaces

Disjoint strict singularity of inclusions between rearrangement invariant spaces

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces