On One Extremal Problem for a Seminorm on the Space $l_1$ with Weight

• Date: 2005
• Main Authors: Radzievskaya, E. I., Radzievskii, G. V., Радзієвськая, О. І., Радзієвський, Г. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3659
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $α=\{α_j\}_{j∈N}$ be a nondecreasing sequence of positive numbers and let $l_{1,α}$ be the space of real sequences $ξ=\{ξ_j\}_{j∈N}$ for which $∥ξ∥_{1,α} := ∑^{∞}_{j=1}α_j|ξ_j| < +∞$. We associate every sequence $ξ$ from $l_{1,α}$ with a sequence $ξ^∗ = \{|ξ_{φ(j)}|\}_{j∈N}$, where $ϕ(·)$...