BOUNDED LINEAR-OPERATORS BETWEEN C-ASTERISK-ALGEBRAS Academic Article uri icon

abstract

  • 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.

published proceedings

  • DUKE MATHEMATICAL JOURNAL

author list (cited authors)

  • HAAGERUP, U., & PISIER, G.

citation count

  • 40

complete list of authors

  • HAAGERUP, U||PISIER, G

publication date

  • September 1993