Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius we develop diverse inequalities involving w_N. also particular cases a fixed N(.), for instance p-Schatten norms. In [A generalization radius. Linear Algebra Appl. 569 (2019)], Abu Omar Kittaneh defined new That is, given norm $N(\cdot)$ on $\bh$, space bounded linear...