In this article, we consider the best polynomial approximation operator defined on an Orlicz-Lorentz space Λ 𝑤,𝜙 generated by an Orlicz function 𝜙 and a nonnegative continuous weight function 𝑤. Then we extend the best polynomial approximation operator from Λ 𝑤,𝜙 to Λ 𝑤,𝜙 ′ , where 𝜙 ′ is the derivative function of 𝜙. In addition, we establish some properties of the extended best polynomial approximation operator.

In this paper, {1}-inverses of a nilpotent matrix as well as matrices above a given nilpotent matrix under the minus partial order are characterized.

In this paper, we consider the best polynomial approximation operator defined on an Orlicz–Lorentz space , and its extension to , where w is a non‐negative continuous weight function and is the derivative of ϕ, which is not required to be an Orlicz function. Our work generalizes a recent result in this field on an Orlicz–Lorentz space generated by an Orlicz function. In addition, we establish some properties and estimates for any extended best polynomial approximation.