Abstract
In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n, and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as well as compute the norm of Copson operators on the well-known matrix domains such as Hilbert and difference sequence spaces. Moreover, in a reverse manner, we investigate the norm of well-known operators on the Copson matrix domains generated with Copson matrices. Through this study we introduce several new inequalities, inclusions, and factorizations for well-known operators.
Highlights
The Copson matrix domain Cpn is the set of all sequences whose Cn-transforms are in the space p; that is,
Let p ≥ 1 and ω denote the set of all real-valued sequences
2 The Copson Banach spaces Cpn and C∞n the sequence spaces Cpn (1 ≤ p < ∞) and C∞n are introduced by using the Copson matrix of order n, and the inclusions, basis, and duals of this matrix domain will investigated
Summary
The Copson matrix domain Cpn is the set of all sequences whose Cn-transforms are in the space p; that is, 2 The Copson Banach spaces Cpn and C∞n the sequence spaces Cpn (1 ≤ p < ∞) and C∞n are introduced by using the Copson matrix of order n, and the inclusions, basis, and duals of this matrix domain will investigated.
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