Pisier–Ringrose inequality

In mathematics, Pisier–Ringrose inequality is an inequality in the theory of C*-algebras which was proved by Gilles Pisier in 1978 affirming a conjecture of John Ringrose. It is an extension of the Grothendieck inequality.

Statement

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Theorem.[1][2] If   is a bounded, linear mapping of one C*-algebra   into another C*-algebra  , then

 

for each finite set   of elements   of  .

See also

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Notes

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  1. ^ Kadison (1993), Theorem D, p. 60.
  2. ^ Pisier (1978), Corollary 2.3, p. 410.

References

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  • Pisier, Gilles (1978), "Grothendieck's theorem for noncommutative C-algebras, with an appendix on Grothendieck's constants", Journal of Functional Analysis, 29 (3): 397–415, doi:10.1016/0022-1236(78)90038-1, MR 0512252.
  • Kadison, Richard V. (1993), "On an inequality of Haagerup–Pisier", Journal of Operator Theory, 29 (1): 57–67, MR 1277964.