Eva Kopecká (University of Innsbruck): Projecting points between subspaces

University of Szeged, Bolyai Institute, Bolyai Seminar

Abstract. Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projection, the iterates converge to the projection of the point onto the intersection of X and Y.
We will explain when a sequence of orthoprojections of a point in a Hilbert space on a finite family of closed subspaces converges at all, and if it does, how fast it converges. We will show how this linear problem is connected to convexity, measure and graph theory.