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1

RUC systems in rearrangement invariant spaces

100%

Dodds P., Semenov E., Sukochev F.

Studia Mathematica

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2002

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tom 151

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nr 2

161-173

EN

We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.

2

The Banach-Saks property in rearrangement invariant spaces

100%

Dodds P., Semenov E., Sukochev F.

Studia Mathematica

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2004

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tom 162

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nr 3

263-294

EN

This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the Banach-Saks property.

3

Banach-Saks properties in symmetric spaces of measurable operators

100%

Dodds P., Dodds T., Sukochev F.

Studia Mathematica

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2007

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tom 178

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nr 2

125-166

EN

We study Banach-Saks properties in symmetric spaces of measurable operators. A principal result shows that if the symmetric Banach function space E on the positive semiaxis with the Fatou property has the Banach-Saks property then so also does the non-commutative space E(ℳ,τ) of τ-measurable operators affiliated with a given semifinite von Neumann algebra (ℳ,τ).

Ograniczanie wyników

3 Studia Mathematica

3 Dodds P.

3 Sukochev F.

2 Semenov E.

1 Dodds T.

1 2007

1 2004

1 2002

RUC systems in rearrangement invariant spaces

The Banach-Saks property in rearrangement invariant spaces

Banach-Saks properties in symmetric spaces of measurable operators