  They proved several properties and introduced some inequalities. We continue
with the study of this generalized numerical radius and we develop diverse
inequalities involving w_N. We also study particular cases with a fixed N(.),
for instance the p-Schatten norms. In ["A generalization of the numerical
radius". Linear Algebra Appl. 569 (2019)], Abu Omar and Kittaneh defined a new
generalization of the numerical radius. That is, given a norm $N(\cdot)$ on
$\bh$, the space of bounded linear operators over a Hilbert space H, and A in
B(H) w_N(A)=sup_{\theta\in \R}N(Re(e^{i\theta}A)). They proved several
properties and introduced some inequalities. We continue with the study of this
generalized numerical radius and we develop diverse inequalities involving
$w_N$. We also study particular cases when N(.) is the p- Schatten norm with
p>1.
