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Interpolation of Cesàro sequence and function spaces

100%
Astashkin S., Maligranda L.
Studia Mathematica
|
2013
|
tom 215
|
nr 1
39-69
EN
The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that $Ces_{p}(I)$ is an interpolation space between $Ces_{p₀}(I)$ and $Ces_{p₁}(I)$ for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, $Ces_{p}[0,1]$ is not an interpolation space between Ces₁[0,1] and $Ces_{∞}[0,1]$.
2
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Structure of Cesàro function spaces: a survey

100%
Astashkin S., Maligranda L.
Banach Center Publications
|
2014
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tom 102
|
nr 1
13-40
EN
Geometric structure of Cesàro function spaces $Ces_p(I)$, where I = [0,1] and [0,∞), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q ∈ [1,∞] such that $Ces_p[0,1]$ contains isomorphic and complemented copies of $l_q$-spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces $Ces_p[0,1]$.
3
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Structure of Rademacher subspaces in Cesàro type spaces

100%
Astashkin S., Maligranda L.
Studia Mathematica
|
2015
|
tom 226
|
nr 3
259-279
EN
The structure of the closed linear span 𝓡 of the Rademacher functions in the Cesàro space $Ces_{∞}$ is investigated. It is shown that every infinite-dimensional subspace of 𝓡 either is isomorphic to l₂ and uncomplemented in $Ces_{∞}$, or contains a subspace isomorphic to c₀ and complemented in 𝓡. The situation is rather different in the p-convexification of $Ces_{∞} $ if 1 < p < ∞.
4
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New examples of K-monotone weighted Banach couples

81%
Astashkin S., Maligranda L., Tikhomirov K.
Studia Mathematica
|
2013
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tom 218
|
nr 1
55-88
EN
Some new examples of K-monotone couples of the type (X,X(w)), where X is a symmetric space on [0,1] and w is a weight on [0,1], are presented. Based on the property of w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X,X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is $t^{1/p}$ for some p ∈ [1,∞], then $X = L_{p}$. At the same time a Banach couple (X,X(w)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X,X(w)) is K-monotone.
5
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Rademacher functions in BMO

81%
Astashkin S., Leibov M., Maligranda L.
Studia Mathematica
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2011
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tom 205
|
nr 1
83-100
EN
The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic $BMO_{d}$ space on [0,1], where they span a complemented subspace isomorphic to l₂. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Pełczyński type alternative with l₂ and c₀ spaces is proved.
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