Norm of Operators on the Generalized Cesàro Matrix Domain

Abstract

Roopaei in [13] has introduced some factorization for the infinite Hilbert matrix and the Cesàro matrix of order n based on the generalized Cesàro matrix. In this research, we investigate the norm of these two operators on the generalized Cesàro matrix domain. Moreover we introduce some factorizations for the Hilbert matrix. Hence the present study is a complement of Roopaei’s research. There are several new Banach spaces who have introduced and studied by using matrix domains of special lower triangular matrices. For more references we encourage the readers to some papers [1, 3, 17, 18] and textbook [2].

Keywords

• hilbert matrix,
• cesàro matrix,
• norm,
• sequence space.