A study of some inequalities involving moments eigenvalues spreads and positive maps

Abstract

In the present thesis entitled A Study of Some Inequalities Involving Moments, newlineEigenvalues, Spreads and Positive Maps we first investigate some inequalities newlinerelated to the first four central moments and present their applications in both matrix newlinetheory and the theory of polynomial equations. Furthermore, we study some inequalities newlinerelated to eigenvalues when all eigenvalues of a complex square matrix are real. newlineLikewise, we derive some inequalities involving positive linear maps and their role in newlinedetermining bounds for matrix eigenvalues and spreads. Additionally, we examine newlinesome inequalities involving eigenvalues and unital positive linear functionals and derive newlinebounds for the spectral radius and spreads of nonnegative matrices. This research newlinebuilds on the foundational work of researchers such as Kadison (1952), Mirsky (1956, newline1957), Wolkowicz and Styan (1980a), Bhatia and Davis (2000), Bhatia and Sharma newline(2012, 2014, 2016, 2022), Drnovand#711;sek (2013, 2021), Sharma et al. (2015, 2018, 2020), newlineand recent contributions from Sharma et al. (2023). newlineix newline