Research Projects

The study of numerical range in the form of quadratic forms was initiated by Hilbert, Hellinger, Toeplitz and others. It has huge applications in various branches of science including modern day quantum information system. Geometric properties of the numerical range and computation of the exact value of the numerical radius of bounded linear operators are rich and interesting area of research. The study of numerical range assists in understanding the behavior of bounded linear operators. For example, the spectrum of a bounded linear operator is always contained in the closure of the numerical range. Therefore, the spectral value of a bounded linear operator can be estimated if the numerical radius is known to us. There are special kinds of operators for which the numerical radius is known to us, but exact value of the numerical radius is still elusive, even for finite-dimensional operators. Thus the estimation of numerical radius of a bounded linear operator still has its own importance. Recently, we studied several results related to the numerical radius of bounded linear operators acting on complex Hilbert space as well as Banach space. In this project PI wish to continue the study in this direction.