Sharp bounds for sums associated to graphs of matrices

@article{Mingo2012SharpBF,
  title={Sharp bounds for sums associated to graphs of matrices},
  author={J. Mingo and R. Speicher},
  journal={Journal of Functional Analysis},
  year={2012},
  volume={262},
  pages={2272-2288}
}
  • J. Mingo, R. Speicher
  • Published 2012
  • Mathematics
  • Journal of Functional Analysis
  • We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form Sπ(N):=∑j1,…,j2m=1kerj⩾πNtj1j2(1)tj3j4(2)⋯tj2m−1j2m(m) where some of the summation indices are constrained to be equal. The upper bound is easily obtained from a graph Gπ associated to the constraints, π, in the sum. 

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