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    Martingale inequalities and Operator space structures on LpL_p

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    We describe a new operator space structure on LpL_p when pp 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 OHOH, and the square function of a martingale difference sequence dnd_n is Σ dnβŠ—dΛ‰n\Sigma \ d_n\otimes \bar d_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 LpL_p-spaces with analogous results.Comment: Minor corrections. Paper will appear in Documenta Mat
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