MARTINGALE INEQUALITIES AND OPERATOR SPACE STRUCTURES ON L-p

We describe a new operator space structure on Lp when p is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's martingale inequalities have a very natural form: the span of the Rademacher functions is completely isomorphic to the operator Hilbert space OH, and the square function of a martingale difference sequence dn is dn dn. Various inequalities from harmonic analysis are also considered in the same operator valued framework. Moreover, the new operator space structure also makes sense for non-commutative Lp-spaces associatedto a trace with analogous results. When p and the trace is normalized, this gives us a tool to study the correspondence E E defined as follows: if E B(H) is a completely isometric emdedding then E is defined so that E CB(OH) is also one.

MARTINGALE INEQUALITIES AND OPERATOR SPACE STRUCTURES ON L-p Academic Article