Weak convergence of infinite products of operators in Hadamard spaces
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We first prove the weak convergence of iterates of both products and convex combinations of strongly nonexpansive operators in complete CAT(0) spaces. Then we establish the weak convergence of infinite products of possibly discontinuous approximations to such operators. Our main focus is on nearest point projections.
KeywordsCAT(0) space Convex combination Exact orbit Firmly nonexpansive operator Hadamard space Inexact orbit Infinite product Nearest point projection Strongly nonexpansive operator Weak convergence
Mathematics Subject Classification41A65 47H09 47H14 47J25 47N10
This research was partially supported by the Israel Science Foundation (Grant 389/12), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.
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