Seminar on Analysis
Seminar on Fredholm - Operators
Fredholm operators are perhaps the most important class of linear operators between Banach spaces. The solution theory of associated linear equations is very close to the finite-dimensional one. Qualitatively, this is described by an integer index which can be assigned to any Fredholm operator. The Fredholm index is stable with respect to small perturbations in the operator norm and even invariant with respect to homotopies in spaces of continuous operators. It plays a fundamental role, for example, in the solution theory of partial differential equations, in bifurcation theory, and the famous Atiyah-Singer index theorem.
Prerequisites for the seminar are the basic lectures Analysis I-III and Linear Algebra, as well as basic knowledge of linear operators, e.g. from a lecture on functional analysis.