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. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.
Finite rank operators; continuous extension of trace and determinant; first examples; trace class and Hilbert-Schmidt operators in Hilbert space; nuclear operators in Banach spaces; the Fredholm determinant; possible values of traces and determinants - Perelson algebras; inversion formulas; regularised determinants; Hilbert-Carleman determinants; regularised determinants of higher order; inversion formulas via generalised determinants; determinants of integral operators with semi-separable kernels; algebras without the approximation property. Bibliography; list of symbols.
