Overview

This book deals with the determinants of linear operators in Euclidean, Hilbert, and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc.

We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two-parameter eigenvalue problems, as well as to differential, difference, and functional-differential equations.