The Dual Spaces of Sets of Difference Sequences of Order <Emphasis Type="Italic">m</Emphasis> and Matrix Transformations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The Dual Spaces of Sets of Difference Sequences of Order <Emphasis Type="Italic">m</Emphasis> and Matrix Transformations

Authors:	Eberhard Malkowsky Mursaleen Suthep Suantai

Institution:	(1) Department of Mathematics, University of Giessen, Arndtstrasse 2, D-35392 Giessen, Germany;(2) Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia and Montenegro;(3) Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India;(4) Department of Mathematics, Faculty of Science, 80203, Jeddah, Kindom of Saudi Arabia;(5) Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand

Abstract:	Let $p = {\left( {p_{k} } \right)}^{\infty }_{{k = 0}}$ be a bounded sequence of positive reals, m ∈ ℕ and u be s sequence of nonzero terms. If $x = {\left( {x_{k} } \right)}^{\infty }_{{k = 0}}$ is any sequence of complex numbers we write Δ^(m) x for the sequence of the m–th order differences of x and $\Delta ^{{{\left( m \right)}}}_{u} X = {\left\{ {x = {\left( x \right)}^{\infty }_{{k = 0}} :u\Delta ^{{{\left( m \right)}}} x \in X} \right\}}$ for any set X of sequences. We determine the α–, β– and γ–duals of the sets $\Delta ^{{{\left( m \right)}}}_{u} X$ for X = c ₀(p), c(p), ℓ∞(p) and characterize some matrix transformations between these spaces Δ^(m) X. Research of the first author supported by the German DAAD Foundation (German Academic Exchange Service) Grant No. 911 103 012 8 and the Research Project #1232 of the Serbian Ministry of Science, Technology and Development

Keywords:	difference sequences dual spaces matrix transformations
本文献已被维普 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏