BOUNDED LINEAR-OPERATORS BETWEEN C-ASTERISK-ALGEBRAS
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Let $u:A o B$ be a bounded linear operator between two $C^*$-algebras $A,B$. The following result was proved by the second author. Theorem 0.1. There is a numerical constant $K_1$ such that for all finite sequences $x_1,ldots, x_n$ in $A$ we have $$leqalignno{&maxleft{left|left(sum u(x_i)^* u(x_i) ight)^{1/2} ight|_B, left|left(sum u(x_i) u(x_i)^* ight)^{1/2} ight|_B ight}&(0.1)_1cr le &K_1|u| maxleft{left|left(sum x^*_ix_i ight)^{1/2} ight|_A, left|left(sum x_ix^*_i ight)^{1/2} ight|_A ight}.}$$ A simpler proof was given in [H1]. More recently an other alternate proof appeared in [LPP]. In this paper we give a sequence of generalizations of this inequality.