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Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces

100%
Sukochev F., Zanin D.
Studia Mathematica
|
2009
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tom 191
|
nr 2
101-122
EN
We study the class of all rearrangement-invariant ( = r.i.) function spaces E on [0,1] such that there exists 0 < q < 1 for which $∥∑_{k=1}^{n}ξ_{k}∥_{E} ≤ Cn^{q}$, where ${ξ_{k}}_{k≥1} ⊂ E$ is an arbitrary sequence of independent identically distributed symmetric random variables on [0,1] and C > 0 does not depend on n. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_{p})$, p ≥ 1. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.
2
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Sequences of independent identically distributed functions in rearrangement invariant spaces

100%
Astashkin S., Sukochev F.
Banach Center Publications
|
2008
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tom 79
|
nr 1
27-37
EN
A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.
3
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Orbits in symmetric spaces, II

81%
Kalton N., Sukochev F., Zanin D.
Studia Mathematica
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2010
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tom 197
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nr 3
257-274
EN
Suppose E is fully symmetric Banach function space on (0,1) or (0,∞) or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on f ∈ E so that its orbit Ω(f) is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space.
4
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RUC systems in rearrangement invariant spaces

81%
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.
5
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The Banach-Saks property in rearrangement invariant spaces

81%
Dodds P., Semenov E., Sukochev F.
Studia Mathematica
|
2004
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tom 162
|
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.
6
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Banach-Saks properties in symmetric spaces of measurable operators

81%
Dodds P., Dodds T., Sukochev F.
Studia Mathematica
|
2007
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tom 178
|
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).
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