Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Publish Year: 1391
Type: Journal paper
Language: English
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Document National Code:
JR_IJNAA-3-1_007
Index date: 2 December 2022
Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm abstract
Let A=(a_{n,k})_{n,k\geq1} and B=(b_{n,k})_{n,k\geq1} be two non-negative matrices. Denote by L_{v,p,q,B}(A), the supremum of those L, satisfying the following inequality:\|Ax\|_{v,B(q)}\geq L\|x\|_{v,B(p)},where x\geq 0 and x \in l_p(v,B) and alsov = (v_n)_{n=1}^\infty is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for L_{v,p,q,B}(H_\mu), where H_\mu is the Hausdorff matrix and 0 < q \leq p \leq1. Also for the case p = 1, we obtain \|Ax\|_{v,B(1)}, and for the case p\geq 1, we obtain L_{v,p,q,B}(A).
Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm Keywords:
Lower bound , Weighted block sequence space , Hausdorff matrices , Euler matrices , Cesaro matrices , Matrix norm