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Cauchy-Binet type formulas for Fredholm operators

Ciecierska G.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

43--54

Suppose A ∈ L(Y ,Z ) , B ∈ L(X ,Y ) are Fredholm operators acting in linear spaces. By referring to the correspondence between Fredholm operators and their determinant systems, we derive the formulas for a determinant system for AB which are expressed via determinant systems for A and B. In our approach, applying results of the theory of determinant systems plays the crucial role and yields Cauchy-Binet type formulas. The formulas are utilized in many branches of applied science and engineering.