A new seminorm of $n$-tuple operators and its applications

We introduce a new seminorm of $n$-tuple operators, which generalizes the $A$-Euclidean operator radius of $n$-tuple bounded linear operators on a complex Hilbert space. We introduce and study basic properties of this seminorm. As an application of the present study, we estimate bounds for the $A$-Euclidean operator radius ($A$-joint numerical radius). In addition, we improve on some of the important existing $A$-numerical radius inequalities and related results.