Pisier–Ringrose inequality - Alchetron, the free social encyclopedia

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

Theorem. If γ is a bounded, linear mapping of one C*-algebra A into another C*-algebra B , then

∥ ∑ j = 1 n γ ( A j ) ∗ γ ( A j ) + γ ( A j ) γ ( A j ) ∗ ∥ ≤ 4 ∥ γ ∥ 2 ∥ ∑ j = 1 n A j ∗ A j + A j A j ∗ ∥

for each finite set { A 1 , A 2 , … , A n } of elements A j of A .

References

Pisier–Ringrose inequality Wikipedia

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