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A Discretized Approach to W. T. Gowers' Game

100%

Kanellopoulos V. , Tyros K.

tom 58

nr 1

1-16

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.

Determining c₀ in C(𝒦) spaces

100%

Argyros S. , Kanellopoulos V.

Fundamenta Mathematicae

2005

tom 187

nr 1

61-93

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.

A classification of separable Rosenthal compacta and its applications

92%

Argyros S. , Dodos P. , Kanellopoulos V.

Instytut Matematyczny Polskiej Akademii Nauk