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Weak convergence of infinite products of operators in Hadamard spaces

  • Simeon ReichEmail author
  • Zuly Salinas
Article

Abstract

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.

Keywords

CAT(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 Classification

41A65 47H09 47H14 47J25 47N10 

Notes

Acknowledgments

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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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe Technion-Israel Institute of TechnologyHaifaIsrael

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