Lower bound for the norm of lower triangular matrices on block weighted sequence spaces

Abstract

Let 1 < p < ∞ and A = (a n,k) n,k 1 be a non-negative matrix. Denote by A w,p,F , the infimum of those U satisfying the following inequality: Ax w,p,F U x w,p,I , where x 0 and x ∈ l p (w,I) and also w = (w n) ∞ n=1 is a decreasing, non-negative sequence of real numbers. The purpose of this paper is to give a lower bound for A w,p,F , where A is a lower triangular matrix. In particular, we apply our results to Weighted mean matrices and Nörlund matrices which recently considered in [2,3,6] on the usual sequence spaces. Our results generalize some work of Jameson, Lashkaripour, Frotannia and Chen in [4,7,8].

Norm of matrix operator on Orlicz-binomial spaces and related operator ideal

“…More recently, Manna [26] has studied Orlicz extension of weighted Euler sequence space and obtained norm inequalities involving generalized Hausdorff and Nörlund matrix operators which strengthen the results of Talebi and Dehgan [38]. The lower bounds of operators on different sequence spaces were studied in [18,[21][22][23][24]. Recently Roopaei and Foroutannia [34,35] and Ilkhan [15] discussed the norms of matrix operators on different sequence spaces.…”

Upper bounds for the operator norms of Hausdorff matrices and Nörlund matrices on the Euler weighted sequence space

“…Our result provides an upper estimate for |H μ | p (v),e θ v, p , where 1 < p < ∞ and H μ be the Hausdorff matrix operator (see Theorem 3.2). Euler matrices and Gamma matrices which were recently considered in [2,6] on p , in [7][8][9][10] on p (v) and in [11] on the block weighted sequence space p (v, F). As a consequence, we apply Theorem 3.2 to Cesàro matrices, Hölder matrices, Euler matrices and Gamma matrices.…”