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Published online by Cambridge University Press: 10 February 2020
This chapter starts with an overview of the complex interpolation method, for pairs of Banach spaces. Our main application here is when the pair is formed of the same space X with two equivalent norms. Fix an integer n. We consider a C*-algebra A and the space X formedof n-tuples in A equipped with two norms: the row-norm and the column-norm. In that case we prove a remarkable formula identifying the interpolated norm of parameter 1/2 (the midpoint of the interpolation scale). The latter formula involves the maximal tensor product of A with its complex conjugate. This is a preparation for the next chapter.
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