Commutant lifting theorem

From Wikipedia, the free encyclopedia

The commutant lifting theorem states that if T is a contraction on a Hilbert space H, (U,K) is its minimal unitary dilation (which can be shown to exist by Sz.-Nagy's dilation theorem), and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that

for all

and

[edit] References

• Vern Paulsen, Completely Bounded Maps and Operator Algebras 2002, ISBN 0-521-81669-6