BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX  

作　　者：Feyzi BASAR Hadi ROOPAEI 

机构地区：[1]Department of Primary Mathematics Teacher Education,Inonu University,44280–Malatya,Turkiye [2]Department of Mathematics and Statistics,University of Victoria,Victoria,Canada

出　　处：《Acta Mathematica Scientia》2023年第4期1518-1536,共19页数学物理学报（B辑英文版）

摘　　要：Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).

关 键 词：matrix domain normed sequence space duals and matrix transformations 

分 类 号：O178[理学—数学]