Fredholm theory in paraalgebras

This book is devoted to a generalization of the classical Fredholm theory of operators, namely the Fredholm theory in Banach algebras and paraalgebras. An element in a Banach algebra (or paraalgebra), which is invertible modulo a given ideal, is called a Fredholm element with respect to this ideal and these elements are studied in the present work. In the first chapter the foundations of Fredholm theory in paraalgebras are developed and the following three chapters deal with applications of the abstract theory to interpolation theory, majorized operators and triangular operators. Generally speaking, the examples show that the characterization of abstract Fredholm elements in the various situations lead to properties which fit astonishingly well tu the respective cases and thus characterize a natural class of operators.