Lower Bound for the Norm of Lower Triangular Matrices on Block Weighted Sequence Spaces
نویسندگان
چکیده
Let 1 < p < ∞ and A = (an,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 ∈ lp(w,I) and also w = (wn)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].
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