Traces and determinants of linear operators

by Gohberg, I

This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. All the important classical examples of traces and determinants suggested by Hill, von Koch, Fredholm, Poincaré, Ruston and Grothendieck are exhibited in particular, the determinants which were first introduced by Hill and Poincaré in their investigations of infinite systems of linear equations stemming from problems in celestial mechanics are studied most of Fredholm‘s seminal results are presented in this book. Formulas for traces and determinants in a Hilbert space setting are readily derived and generalizations to Banach spaces are investigated. A large part of this book is also devoted to generalizations of the regularized determinants introduced by Hilbert and Carleman. Regularized determinants of higher order are presented in embedded algebras. Much attention is paid to integral operato