On one extremal problem for numerical series

  • E. I. Radzievskaya
  • G. V. Radzievskii

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 $1 < p < ∞$.
Published
25.10.2005
How to Cite
Radzievskaya, E. I., and G. V. Radzievskii. “On One Extremal Problem for Numerical Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 10, Oct. 2005, pp. 1430–1434, https://umj.imath.kiev.ua/index.php/umj/article/view/3698.
Section
Short communications