We define a new norm called the p-numerical radius of a pair of bounded linear operators on \({\mathcal {B}}_{p}({\mathcal {H}})\times {\mathcal {B}}_{p}({\mathcal {H}})\) , where \({\mathcal {B}}_{p}({\mathcal {H}})\) is the Schatten p-class. We give some bounds for this norm. We apply the properties of this norm to deduce several bounds for the p-numerical radii of \(2\times 2\) operator matrices. Also, we investigate the transition between this norm and the p-numerical radius of a single operator.
