A new type of Numerical radius of operators on Hilbert $C^{\ast }$-module

Abstract

In this paper, we define a new concept of numerical range $W_o(\cdot )$ and prove its basic results. We also define the numerical radius ${\omega }_o(\cdot )$ and prove that $${\omega }_o(T)\le |||T|||\le 2{\omega }_o(T).$$