Executive Summary : | The study of the numerical range and radius of an operator acting over Hilbert spaces is a fundamental problem in operator theory, particularly in quantum physics. The C*-algebra was developed to model observables of quantum physics, and authors have considered the numerical range and radius of an element in C*-algebra. This proposed project aims to study and estimate the numerical radius in a C*-algebra setting, focusing on the joint numerical radius of a tuple of elements in C*-algebra. The project will also focus on a partially solved conjecture related to the joint numerical radius of a tuple of operators. The Davis-Wielandt shell and its radius, which summarizes information about the point spectrum, numerical range and radius, and other spectral sets, will be analyzed for an element of C*-algebra. The project will also focus on the q-numerical range, which generalizes the corresponding results of numerical radius. The estimations of numerical radius, joint numerical radius, and Davis-Wielandt radius in the C*-algebra setting will help approximate the spectrum, joint spectrum, and spectral radius, which can be used in quantum physics, particularly in quantum uncertainty relations. |