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There is a numerical constant $K_1$ such that for all finite sequences $x_1,\\ldots, x_n$ in $A$ we have $$\\leqalignno{&\\max\\left\\{\\left\\|\\left(\\sum u(x_i)^* u(x_i)\\right)^{1/2}\\right\\|_B, \\left\\|\\left(\\sum u(x_i) u(x_i)^*\\right)^{1/2}\\right\\|_B\\right\\}&(0.1)_1\\cr \\le &K_1\\|u\\| \\max\\left\\{\\left\\|\\left(\\sum x^*_ix_i\\right)^{1/2}\\right\\|_A, \\left\\|\\left(\\sum x_ix^*_i\\right)^{1/2}\\right\\|_A\\right\\}.}$$\n  A simpler proof was given in [H1]. 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