科研之友
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摘要
We describe a new operator space structure on L-p 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 d(n) is Sigma d(n) circle times (d) over bar (n). 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 L-p-spaces associated to a trace with analogous results. When p -> infinity and the trace is normalized, this gives us a tool to study the correspondence E bar right arrow (E) under bar defined as follows: if E subset of B(H) is a completely isometric emdedding then E is defined so that (E) under bar subset of B(OH) is also one.
- 出版日期2014
