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Determining c₀ in C(𝒦) spaces

S. A. Argyros, V. Kanellopoulos (2005)

Fundamenta Mathematicae

For a countable compact metric space and a seminormalized weakly null sequence (fₙ)ₙ in C() 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 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 generated by (fₙ)ₙ, there exists β ≤ α such that a sequence of β-blocks...

Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2015)

Annales UMCS, Mathematica

We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (Xν) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach-Saks property, then the deviation from the weak Banach-Saks property of an operator of a certain class between direct sums E(Xν) is equal to the supremum of such deviations attained on the coordinates Xν. This is a quantitative version for operators of the result...

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