On the Sequential (p, δ, τ)-Numerical Radius Function of Operator Sequence

In this article, firstly, some basic properties of the sequential (p,δ,τ)-numerical radius function are investigated. The relationships between the sequential (p,δ,τ)-numerical radius of an operator sequence and the sequential (p,δ,τ)-numerical radii of its coordinate operators are analyzed. Then, the relationships between the sequential (p,δ,τ)-numerical radius of an operator sequence and the sequential (p,δ,τ)-numerical radii of its real and imaginary parts are presented. Finally, this analysis is extended to the case in which the coordinate operators are sectorial, providing additional insight into the structural behavior of the sequential (p,δ,τ)-numerical radius function. The obtained results are generalized to some well-known famous results about the numerical radius function from the recent literature. Also, an important contribution is made to the existing literature via different and useful results.