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1
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Determining c₀ in C(𝒦) spaces

100%
Argyros S., Kanellopoulos V.
Fundamenta Mathematicae
|
2005
|
tom 187
|
nr 1
61-93
EN
For a countable compact metric space 𝒦 and a seminormalized weakly null sequence (fₙ)ₙ in C(𝒦) we provide some upper bounds for the norm of the vectors in the linear span of a subsequence of (fₙ)ₙ. These bounds depend on the complexity of 𝒦 and also on the sequence (fₙ)ₙ itself. Moreover, we introduce the class of c₀-hierarchies. We prove that for every α < ω₁, every normalized weakly null sequence (fₙ)ₙ in $C(ω^{ω^{α}})$ and every c₀-hierarchy 𝓗 generated by (fₙ)ₙ, there exists β ≤ α such that a sequence of β-blocks of (fₙ)ₙ is equivalent to the usual basis of c₀.
2
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A Discretized Approach to W. T. Gowers' Game

100%
Kanellopoulos V., Tyros K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2010
|
tom 58
|
nr 1
1-16
EN
We give an alternative proof of W. T. Gowers' theorem on block bases by reducing it to a discrete analogue on specific countable nets. We also give a Ramsey type result on k-tuples of block sequences in a normed linear space with a Schauder basis.
3
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A classification of separable Rosenthal compacta and its applications

88%
Argyros S., Dodos P., Kanellopoulos V.
Instytut Matematyczny Polskiej Akademii Nauk
4
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Higher order spreading models

81%
Argyros S., Kanellopoulos V., Tyros K.
Fundamenta Mathematicae
|
2013
|
tom 221
|
nr 1
23-68
EN
We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_{s})_{s∈ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy $(𝒮ℳ_{ξ}(X))_{ξ<ω₁}$. Each $𝒮ℳ_{ξ}(X)$ contains all spreading models generated by ℱ-sequences $(x_{s})_{s∈ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.
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