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On one extremal problem for numerical series

Authors:

E I Radzievskaya G V Radzievskii

Institution:

(1) National University of Food Technology, Kyiv

Abstract:

Let Γ be the set of all permutations of the natural series and let α = {α _j}_j∈ℕ, ν = {ν_j}_j∈ℕ, and η = {η_j}_j∈ℕ be nonnegative number sequences for which

$\left\| {\nu (\alpha \eta )_\gamma } \right\|_1 : = \sum\limits_{j = 1}^\infty {v _j \alpha _{\gamma (_j )} } \eta _{\gamma (_j )}$

is defined for all γ:= {γ(j)}_j∈ℕ ∈ Γ and η ∈ l _p. We find $\sup _{\eta :\left\| \eta \right\|_p = 1} \inf _{\gamma \in \Gamma } \left\| {\nu (\alpha \eta )_\gamma } \right\|_1$ in the case where 1 < p < ∞. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005.

Keywords:

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