Weighted means and Karcher equations of positive operators.

@article{Lawson2013WeightedMA,
  title={Weighted means and Karcher equations of positive operators.},
  author={Jimmie Lawson and Yongdo Lim},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={2013},
  volume={110 39},
  pages={15626-32}
}
The Karcher or least-squares mean has recently become an important tool for the averaging and study of positive definite matrices. In this paper, we show that this mean extends, in its general weighted form, to the infinite-dimensional setting of positive operators on a Hilbert space and retains most of its attractive properties. The primary extension is via its characterization as the unique solution of the corresponding Karcher equation. We also introduce power means in the infinite… CONTINUE READING

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