A NORM CONVERGENCE RESULT ON RANDOM PRODUCTS OF RELAXED PROJECTIONS IN HILBERT-SPACE

Suppose X is a Hilbert space and C-1, ..., C-N are closed convex inter secting subsets with projections P-1, ..., P-N. Suppose further r is a mapping from N onto {1, ..., N} that assumes every value infinitely o ften. We prove (a more general version of) the following result: If th e N-tuple (C-1, ..., C-N) is ''innately boundedly regular'', then the sequence (x(n)), defined by x(0) is an element of X arbitrary, x(n+1) := P-r(n)x(n), for all n greater than or equal to 0, converges in norm to some point in boolean AND(i=1)(N) C-i. Examples without the usual assumptions on compactness are given. Methods of this type have been u sed in areas like computerized tomography and signal processing.