Introduction

As in the finite dimensional case, determinants of operators acting on infinite dimensional Banach spaces provide important tools for solving linear equations by exhibiting explicit formulas for their solutions. These formulas are generalizations of the famous Cramer’s rule for solving finite systems of linear equations. The most outstanding example is Fredholm’s theory of integral equations. By means of determinants, Fredholm was able to exhibit explicit solutions of the equations and to determine additional properties of the integral operators such as the existence of eigenvalues and the evaluation of their multiplicities [Fr].