Bounded linear operators between C^*-algebras

1993/02/18 by Haagerup, U., Pisier, Gilles · 5 citations
#47C #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9302214

Abstract

Let u:A→ 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 K₁ such that for all finite sequences x₁,…, x_n in A we have \leqalignnoamp;max\‖(∑ u(x_i)^* u(x_i))^1/2‖_B, ‖(∑ u(x_i) u(x_i)^*)^1/2‖_B\amp;(0.1)₁\cr ≤ amp;K₁‖u‖ max\‖(∑ x^*_ix_i)^1/2‖_A, ‖(∑ x_ix^*_i)^1/2‖_A\. 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.

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